For the first time a hybrid semiconductor photon counting pixel detector has been used for measurements of linear X-ray polarization by exploiting the Compton effect in the silicon sensor layer. The time-to-shutter mode of the X-ray imaging detector Timepix was used to identify Compton scattering events in the sensor layer by the analysis of coincidences. For irradiation with polarized X-ray photons of energies between 27 and 84 keV we were able to measure a large modulation factor of μmeas = (68.1±16.4) % for this type of X-ray polarimeter. Degree and orientation of linear polarization can be determined. This publication describes experimental setup, data analysis method, measurement and simulation results, and gives first estimations Preprint submitted to Elsevier August 14, 2008 on the polarimetric performance for an application in X-ray astronomy.