We present the calculation on the performance of a High Gain Harmonic Generation (HGHG) X-ray Free Electron Laser (FEL) based on the high quality electron beam from the proposed Photoinjected Energy Recovery Linac (PERL) at the NSLS. We consider several sets of e-beam parameters. The calculation indicates that it is possible to produce a fully coherent FEL with a wavelength around 10 Angstrom, with a peak power of several GW. The high order harmonics will also be produced with a significant amount of peak power. One further attractive feature is the possibility to produce ultra short radiation pulses of about 10 fs based on such HGHG scheme.