The ability to specifically engineer the genome of living cells at precise locations using rare-cutting designer endonucleases has broad implications for biotechnology and medicine, particularly for functional genomics, transgenics and gene therapy. However, the potential impact of chromosomal context and epigenetics on designer endonuclease-mediated genome editing is poorly understood. To address this question, we conducted a comprehensive analysis on the efficacy of 37 endonucleases derived from the quintessential I-CreI meganuclease that were specifically designed to cleave 39 different genomic targets. The analysis revealed that the efficiency of targeted mutagenesis at a given chromosomal locus is predictive of that of homologous gene targeting. Consequently, a strong genome-wide correlation was apparent between the efficiency of targeted mutagenesis (≤ 0.1% to ≈ 6%) with that of homologous gene targeting (≤ 0.1% to ≈ 15%). In contrast, the efficiency of targeted mutagenesis or homologous gene targeting at a given chromosomal locus does not correlate with the activity of individual endonucleases on transiently transfected substrates. Finally, we demonstrate that chromatin accessibility modulates the efficacy of rare-cutting endonucleases, accounting for strong position effects. Thus, chromosomal context and epigenetic mechanisms may play a major role in the efficiency rare-cutting endonuclease-induced genome engineering.