Contextuality is a phenomenon at the heart of the quantum mechanical departure from classical behavior, and has been recently identified as a resource in quantum computation. Experimental demonstration of contextuality is thus an important goal. The traditional form of contextuality—as violation of a Kochen–Specker inequality—requires a quantum system with at least three levels, and the status of the assumption of determinism used in deriving those inequalities has been controversial. By considering “unsharp” observables, Liang, Spekkens, and Wiseman (LSW) derived an inequality for generalized noncontextual models that does not assume determinism, and applies already to a qubit. We experimentally implement the LSW test using the polarization states of a heralded single photon and three unsharp binary measurements. We violate the LSW inequality by more than 16 standard deviations, thus showing that our results cannot be reproduced by a noncontextual subset of quantum theory.