A phase chaos synchronization of semiconductor lasers with open-loop unidirectional coupling is studied. The phase time series of chaotic laser field is extracted using a Hilbert transform, and the phase synchronization characteristic is analyzed by a cross correlation coefficient and synchronization error. The results of the experiment show that the master laser and slave laser can attain a phase chaos synchronization with a synchronization coefficient above 0.95 at an injection strength exceeding 0.80 and its frequency detuning from -11 GHz to 4 GHz. The results also show that phase chaos synchronization has a wider parameter range than intensity chaos synchronization. According to the average phase difference, the phase-locking phenomenon is also observed during the experiment.