Most models of ambiguity aversion satisfy Anscombe-Aumann's Monotonicity axiom. This paper proposes a test of Monotonicity, the Allais Horse Race. It is an adaptation of the Allais paradox to a setting with both subjective and objective uncertainty. Viewed as a thought experiment, the Allais Horse Race allows for introspective assessment of Monotonicity. Implementing it as an incentivized experiment, we find that the modal choice of subjects violates Monotonicity in a specific, intuitive way. Overall, we find that models of ambiguity aversion that satisfy Monotonicity cannot describe the behavior of about half of all subjects.