Singly quantized vortices have been already observed in many systems including the superfluid helium, Bose Einstein condensates of dilute atomic gases, and condensates of exciton polaritons in the solid state. Two dimensional superfluids carrying spin are expected to demonstrate a different type of elementary excitations referred to as half quantum vortices characterized by a pi rotation of the phase and a pi rotation of the polarization vector when circumventing the vortex core. We detect half quantum vortices in an exciton-polariton condensate by means of polarization resolved interferometry, real space spectroscopy and phase imaging. Half quantum vortices coexist with single quantum vortices in our sample.