We have undertaken a survey, the Deep X-Ray Radio Blazar Survey (DXRBS), of archived, pointed ROSAT Position Sensitive Proportional Counter data for blazars by correlating the ROSAT WGACAT database with several publicly available radio catalogs, restricting our candidate list to serendipitous flat radio spectrum sources (α r≤ 0.70, where S ν∝ ν). We discuss our survey methods, identification procedure, and first results. Our survey is found to be∼ 95% efficient at finding flat-spectrum radio-loud quasars (FSRQs; 59 of our first 85 identifications) and BL Lacertae objects (22 of our first 85 identifications), a figure that is comparable to or greater than that achieved by other radio and X-ray survey techniques. The identifications presented here show that all previous samples of blazars (even when taken together) did not representatively survey the blazar population, missing critical regions of (L X, L R) parameter space within which large fractions of the blazar population lie. Particularly important is the identification of a large population of FSRQs (≳ 25% of DXRBS FSRQs) with ratios of X-ray to radio luminosity≳ 10-6 (α rx≲ 0.78). In addition, as a result of our greater sensitivity, the DXRBS has already more than doubled the number of FSRQs in complete samples with 5 GHz (radio) luminosities between 10 31.5 and 10 33.5 ergs s-1 Hz-1, and fills in the region of parameter space between X-ray–selected and radio-selected samples of BL Lac objects. The DXRBS is the very first sample to contain statistically significant numbers of blazars at low luminosities, approaching what should be the lower end of the FSRQ luminosity function.