The repurposed CRISPR-Cas9 system has recently emerged as a revolutionary genome-editing tool. Here we report a modification in the expression of the guide RNA (gRNA) required for targeting that greatly expands the targetable genome. gRNA expression through the commonly used U6 promoter requires a guanosine nucleotide to initiate transcription, thus constraining genomic-targeting sites to GN19NGG. We demonstrate the ability to modify endogenous genes using H1 promoter-expressed gRNAs, which can be used to target both AN19NGG and GN19NGG genomic sites. AN19NGG sites occur ~15% more frequently than GN19NGG sites in the human genome and the increase in targeting space is also enriched at human genes and disease loci. Together, our results enhance the versatility of the CRISPR technology by more than doubling the number of targetable sites within the human genome and other eukaryotic species.