Can I legally omit the fact I hold a Ph.D. degree? I am about to complete a Ph.D. in Hong Kong and would like to study in the United States. I hold a first class B.Eng. degree in Electrical Engineering. I have a CGPA of 3.67 out of 4 in my current PhD studies, two journal publications (IEEE Transactions) with two more to be submitted soon. I would consider this a fairly good academic record.

For career purposes, I would like to obtain a Ph.D. degree (in a different but related field) from a top American university. There aren't post-doc openings in my current research area, which is why I am considering another PhD in a related area.

Question: Is it considered illegal to not mention that I hold a Ph.D. (hopefully) during application? I noticed some schools frown at what some would call a "professional" or "serial" student. 

NB: I have read responses on this question and I am satisfied with them. But I feel there's need to make my question clearer for those who did not understand. Some universities clearly state on their websites that they will not consider applicants who already hold a Ph.D. while some others do not specify this. My question was more for the latter. But now I know that other than dealing with the university, it will require lying on visa application, as some people wrote below.

Thank you all for your contributions.
No. You cannot hide such a fact in US admissions processes. Lying about your previous academic record—whether by omission or by claiming false credentials—is sufficient reason to revoke an offer of admission if it is caught before the applicant matriculates, or grounds to expel a student if caught after enrollment. Depending on the magnitude of the fraud, you may even be asked to pay restitution for the funds spent.

As far as if it’s illegal, that’s a trickier issue. It basically comes down to money: if you received funding based on a misrepresentation or fraudulent application, then it’s far more likely that you’ll face civil or criminal penalties.