  Contextuality is a phenomenon at the heart of the quantum mechanical
departure from classical behaviour, 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 doesn't 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.
