The completeness axiom of choice has been questioned for long, and in response, theoretical models of decision making allowing for incomplete preferences have been developed. So far the theoretical accomplishments have however not been paired with empirical evidence on the actual existence of incomplete preferences. In this paper we provide empirical evidence in support of the existence of incomplete preferences due to multiple priors over an ambiguous event. We design experimental decision tasks where specific choice patterns are consistent with incomplete preferences under uncertainty but inconsistent with models assuming complete preferences. We find that approximately half of the subjects behave consistent with incomplete preferences due to multiple priors and that the observed behavioral pattern cannot be attributed to mistakes, probability weighting or regret aversion. In a robustness test we show that the observed behavior is robust to a prize variation in the ambiguous prospect and consistent with comparative statics predictions based on incomplete preferences under uncertainty.