We study individual demand for COVID-19 antibody tests in an incentivized study on a representative sample of the US population. Almost 2,000 participants trade off obtaining an athome test kit against money. At prices close to zero, 80 percent of individuals want the test. However, this broad support of testing falls sharply with price. Demand decreases by 19 percentage points per $10 price increase. Demand for testing increases with factors related to its potential value, such as age, increased length and strength of protective immunity from antibodies, and greater uncertainty about having had the virus. Willingness to pay for antibody tests also depends on income, ethnicity and political views. Black respondents show significantly lower demand than white and Hispanic respondents, and Trump-supporters demonstrate significantly lower demand for testing. The results suggest that charging even moderate prices for antibody tests could widen health inequalities.