The FIRST radio survey provides a new resource for constructing a large quasar sample. With source positions accurate to better than 1" and a point source sensitivity limit of 1 mJy, it reaches 50 times deeper than previous radio catalogs. We report here on the results of the pilot phase for a FIRST Bright Quasar Survey (FBQS). Based on matching the radio catalog from the initial 300 deg^2^ of FIRST coverage with the optical catalog from the Automated Plate Machine (APM) digitization of Palomar Sky Survey plates, we have defined a sample of 219 quasar candidates brighter than E = 17.50. We have obtained optical spectroscopy for 151 of these and classified 25 others from the literature, yielding 69 quasars or Seyfert 1 galaxies, of which 51 are new. identifications. The brightest new quasar has an E magnitude of 14.6 and z = 0.91; four others are brighter than E = 16. The redshifts range from z = 0.12 to 3.42. Half of the detected objects are radio quiet with L_21-cm_ < 10^32.5^ ergs/s. We use the results of this pilot survey to establish criteria for the FBQS that will produce a quasar search program which will be 70% efficient and 95% complete to a 21-cm flux density limit of 1.0 mJy.