We have developed a new procedure to search for carbon-enhanced metal-poor (CEMP) stars from the Hamburg/ESO (HES) prism-survey plates. This method employs an extended line index for the CH G band, which we demonstrate to have superior performance when compared to the narrower G-band index formerly employed to estimate G-band strengths for these spectra. Although CEMP stars have been found previously among candidate metal-poor stars selected from the HES, the selection on metallicity undersamples the population of intermediate-metallicity CEMP stars (–2.5 ≤ [Fe/H] ≤ –1.0); such stars are of importance for constraining the onset of the s-process in metal-deficient asymptotic giant branch stars (thought to be associated with the origin of carbon for roughly 80% of CEMP stars). The new candidates also include substantial numbers of warmer carbon-enhanced stars, which were missed in previous HES searches for carbon stars due to selection criteria that emphasized cooler stars. A first subsample, biased toward brighter stars (B< 15.5), has been extracted from the scanned HES plates. After visual inspection (to eliminate spectra compromised by plate defects, overlapping spectra, etc., and to carry out rough spectral classifications), a list of 669 previously unidentified candidate CEMP stars was compiled. Follow-up spectroscopy for a pilot sample of 132 candidates was obtained with the Goodman spectrograph on the SOAR 4.1 m telescope. Our results show that most of the observed stars lie in the targeted metallicity range, and possess prominent carbon absorption features at 4300 Å. The success rate for the identification of new CEMP stars is 43% (13 out of 30) for [Fe/H] < –2.0. For stars with [Fe/H] < –2.5, the ratio increases to 80% (four out of five objects), including one star with [Fe/H] < –3.0.