Illegal based on what? The Constitution is mute on the issue. Supreme Court decisions also have never explicitly stated a definition.
Numerous sources CLAIM no Supreme Court decisions never explicitly stated a definition, but other sources provide citations that did confirm the definition as the same used by Vattel in The Law of Nations.
The Democrats were so convinced by those Federal Court decisions and the Constitution, they pursued Chester Arthur for years with the allegation that he was not eligible for the Office of the Vice President or the Office of the President. Unfortunately, they followed false leads and failed to discover the real evidence of ineligibility.
Chester Arthur, however, gave every appearance of knowing full well that he was ineligible and illegal when he purposefully set out to destroy his public and private papers which could have revealed his ineligibility and illegality.
As recently as the past twelve years the U.S. Congress introduced unsuccessful bills for a Constitutional Amendment that would remove the natural born citizen requirement for eligibility. If Congress did not believe the natural born citizen requirement excluded some native born U.S. citizens from eligibility, there would have been no reason for them to have found it necessary to introduce bills amending the Constitution to remove the natural born citizen requirement.