With our detection of the BL Lac objects Markarian 421 and Markarian 501, the Whipple Collaboration initiated a survey of BL Lac objects with the 10m gamma-ray telescope at the Whipple Observatory in Arizona which has an energy threshold of ~ 300 GeV. The survey consists of observations of all BL Lac objects with known redshifts z < 0.1 and declinations which make them visible in the Northern Hemisphere. We are also in the midst of a survey of X-ray selected BL Lac objects between z=0.1-0.2. We concentrate on nearby BL Lac objects to reduce the effects of interaction between the very high energy gamma rays and background intergalactic infrared radiation fields. We choose X-ray selected BL Lac objects for the survey of more distant BL Lacs, because the gamma-ray spectra for this class of BL Lac objects are expected in most models to extend to higher energies than the radio-selected BL Lac objects more often seen by EGRET. We will present the current status of this survey at this symposium and its implications for understanding this class of blazar.