We have undertaken a survey of archived, pointed ROSAT PSPC 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 (alpha_r <= 0.70). Here 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 IDs) and BL Lacertae objects (22 of our first 85 IDs), a figure which 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 (alpha_rx <~ 0.78). In addition, due to our greater sensitivity, 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 erg/s/Hz and fills in the region of parameter space between X-ray selected and radio-selected samples of BL Lacs. 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.
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