We present results of a survey of CCS, HC 3 N, and HC 5 N toward 40 dark cloud cores to search for "Carbon-Chain-Producing Regions(CCPRs)", where carbonchain molecules are extremely abundant relative to NH 3 , as in L1495B, L1521B, L1521E, and the cyanopolyyne peak of TMC-1. We have mainly observed toward cores where the NH 3 lines are weak, not detected, or not observed in previous surveys, and the CCS, HC 3 N, and HC 5 N lines have been detected toward 17, 17, and 5 sources, respectively. Among them, we have found a CCPR, L492, and its possible candidates, L1517D, L530D, L1147, and L1172B. They all show low abundance ratios of [NH 3 ]/[CCS] (hereafter called the NH 3 /CCS ratio) indicating the chemical youth. Combining our results with those of previous surveys, we have found a significant variation of the NH 3 /CCS ratio among dark cloud cores and among molecular cloud complexes. Such a variation is also suggested by the detection rates of carbon-chain molecules. For instance, the NH 3 /CCS ratios are higher and the detection rates of carbon-chain molecules are lower in the Ophiuchus cores than in the Taurus cores. An origin of these systematic abundance variation is discussed in terms of the difference in the evolutionary stage or the contraction timescale. We have also identified a carbon-chain-rich star-forming core, L483, where intense HC 3 N and HC 5 N lines are detected. This is a possible candidate for a core with "Warm Carbon-Chain Chemistry".