Do you feel threatened or influenced? If the son is at your university and eligible to enroll in a course in the parent's department, then someone has to teach it. So there doesn't seem to be any reason for you to feel uncomfortable with "being placed in this position," unless the parent is trying to influence you.

One should not be deprived of education because who their parents are... But of course there are still ethics (and optics) considerations.

The faculty members I’ve known with kids attending their university were very careful not to have any indication of influence, whether in their department or not. Did something happen previously to lead you to think there may be an issue?

My belief, as someone in the situation, is that there is at least a perceived conflict of interest on the part of this administrator who admitted his son into the program where he is the boss of every faculty member. The son should either be in a different major at the same university, or in the same major at a different university. I'm comfortable asserting "perceived conflict of interest" because I'm perceiving one. I also believe that perceived conflicts of interest are just as bad as "real ones" in cases where there is insufficient information to demarcate between the two types.

Where in the world are you, and what kind of program is this? In the US, at the bachelor's level, it is quite uncommon for a departmental chair to have much (if any) influence on the admissions process---students are typically admitted to the college, but are free to select a major within that college at their discretion. At the graduate level, a chair can exert some influence, but would be well-advised to recuse themselves. Are you certain that (a) your chair has such influence, and (b) exercised that influence on behalf of their child?

@XanderHenderson - many smaller universities actually offer free tuition for dependents as part of a faculty benefits package, including fairly easy entrance.

What actual power does your department chair hold? This varies strongly between universities and even departments. For example, at my university, the position is rotated every year and volunteering disqualifies you from the job.

academia.stackexchange.com/a/115356 may be relevant

Knowing the country where this happens could help getting more focused answers. Although general ethics principles may be transnational, local culture, practice and laws varies wildly across countries.

@JonCuster Thanks for pointing that out. Indeed, my own institution (a small community college in rural Arizona) offers free tuition for one class per semester to any dependent or spouse of a college employee. I have taught colleagues' children on several occasions since starting this position two years ago, and suspect that the only reason I have not taught the children of supervisors is that all of their children have already moved on.

The question which you have actually posed here is about the ethics implications of this situation. The answers which have gotten largely seem to converge on the notion that there is no a priori ethical problem here. In your responses to several people, you have emphasized the fact that you are uncomfortable about this situation. Is the mere relationship problematic, or have you seen this chair behave in a way that is unethical? There is a world of difference between a chair being placed in a position where they have the potential to act unethically, and them actually doing so.

By way of analogy, I could just as easily ask a question like the following: "I am the TA in a class. A lot of the students in this class are the kind of people that the primary instructor of the class finds sexually attractive. I am worried that my supervisor will become sexually involved with one of these students. What are the ethical considerations here?" The answer is that there is no a priori ethical problem, and the instructor is responsible for their own actions. If they actually behave in a manner which is inappropriate, then there are actions that you can take.

So, again: is this a hypothetical ("I am uncomfortable because I believe that my boss might try to exert influence"), or is there an actual transgression which has occurred ("My boss tried to get me to change the grade of their child")? If the former, then remain vigilant, but don't go looking for trouble where it doesn't exist. If the latter, then this isn't the correct forum---you need to talk to a higher administrator, a union rep, an ombud, an employment lawyer, or someone else in a position to correct the existing ethical breach.

I don't buy the analogies just attempted. Much closer analogies are available -- to situations where "the power dynamic" and "power differentials" are brought in as key elements. These things certainly exist "a priori" in my situation.

I will repeat my question: has an actual ethical violation occurred, or are you simply worried about a hypothetical future ethical violation?

I will repeat my previous answer: the issue is about a coming semester, although concerns were stated about the impropriety of the same situation over the past two semesters. By your reasoning, ALL concerns over power differentials should simply be dismissed since "nothing bad has happened yet."

That doesn't answer my question. Has an actual ethical violation occurred? "Concerns being stated" does not constitute an ethical breach. Is there evidence that your chair is behaving unethically?

Regarding the edit to your comment: I have never dismissed the concern over the power dynamic. I have repeatedly stated that there is no a priori ethical problem here, but that if an ethical breach occurs, there are things that you can do about it. Everything that you have stated about this situation is vague, nebulous, and seemingly hypothetical. In the abstract, there is no a priori ethical violation if a student takes a class in a program where their parent is an administrator.

The point (in my view) would be to build adequate safeguards into such situations in order to prevent anything from going wrong. The fact that no one drove or fell off a given bridge does not mean that safety rails shouldn't be there. Your argument has consistently been that "nothing is wrong since nobody fell off the side of that particular bridge yet." I believe the situation itself is unwise and concerning, and I've certainly felt pressures that I never before experienced as a faculty member.

How do you know that such safeguards don't exist? Does your institution not have a set of policies and procedures for dealing with this kind of thing? My own institution, which is tiny has a set of policies and procedures for dealing with grievances. If an administrator were to abuse their position in order to advance their child, it would be fairly straightforward for me to file a grievance. But this is dependent upon the administrator actually misbehaving. If everyone acts appropriately, there is no problem.

However, I can see that our views are not reconcilable and I'm happy that you and others have apparently been in this situation multiple times with no negative effects.

Also, the fact that you characterize my response as "nothing is wrong since nobody fell of the side of that particular bridge yet" seems to indicate that you aren't reading what I am writing, or that I am failing to communicate. I have repeatedly stated that there is not an a priori ethical problem here, but that if a problem occurs, there are procedures which exist to mitigate the problem. But if no problem has actually occurred, why catastrophize?

On what basis have you asserted that "there are procedures which exist to mitigate the problem"? Because they exist at your workplace?

Perhaps it is time for you to read your faculty handbook, and seek out your institution's policies with regard to ethical practice (and, maybe, their procedures for filing a grievance).

More here, from the HLC: "The institution has ethics policies for faculty and staff regarding conflict of interest, nepotism, recruitment and admissions, financial aid, privacy of personal information, and contracting." (emph added) and "The institution establishes and publicizes clear procedures for receiving complaints from students and other constituencies, responding to complaints in a timely manner, and analyzing complaints to improve its processes. The institution does not retaliate against those who raise complaints."