CRISPR-Cas9 nucleases are widely used for genome editing but can induce unwanted off-target mutations. Existing strategies for reducing genome-wide off-target effects of the widely used Streptococcus pyogenes Cas9 (SpCas9) are imperfect, possessing only partial or unproven efficacies and other limitations that constrain their use. Here we describe SpCas9-HF1, a high-fidelity variant harbouring alterations designed to reduce non-specific DNA contacts. SpCas9-HF1 retains on-target activities comparable to wild-type SpCas9 with > 85% of single-guide RNAs (sgRNAs) tested in human cells. Notably, with sgRNAs targeted to standard non-repetitive sequences, SpCas9-HF1 rendered all or nearly all off-target events undetectable by genome-wide break capture and targeted sequencing methods. Even for atypical, repetitive target sites, the vast majority of off-target mutations induced by wild-type SpCas9 were not detected with SpCas9-HF1. With its exceptional precision, SpCas9-HF1 provides an alternative to wild-type SpCas9 for research and therapeutic applications. More broadly, our results suggest a general strategy for optimizing genome-wide specificities of other CRISPR-RNA-guided nucleases.