In addition to specific inquiries about race and Spanish origin, the censuses of 1980 and 1990 included an open-ended question about ancestry, which replaced the question about parents' place of birth that had been used since 1870. This paper examines findings from the new ancestry question from the perspective of measuring ethnicity. The question adds little information about Hispanics, racial minorities, or recent immigrants, who can be identified readily on the basis of other census inquiries. The ancestry question allows us to characterize the descendants of European immigrants, but because of ethnic intermarriage, the numerous generations that separate present respondents from their forebears, and the apparent unimportance of ancestry to many whites of European origin, responses appear quite inconsistent. In regard to these groups, we may now be in an era of optional ethnicity, in which no simple census question will distinguish those who identify strongly with a specific European group from those who report symbolic or imagined ethnicity.