Isotopic abundance ratios of carbon and oxygen have been determined for the local interstellar medium by observations of carbon monoxide in three dark clouds. The 12C/13C ratio is obtained by measurements of the optically thin species 12C18O and 13C18O. The weighted mean ratio for the sources B5, B335, and L1262 is found to be 75+-8 (1 sigma), close to the solar system value of 89. From C17O data we find that 18O/17O = 2.8+-0.2, a factor of 2 smaller than the solar system value. The weighted mean double ratio (13C/12C)(16O/18O) is determined from the J=1-0 and J=2-1 13CO and C18O lines to be 7.0+-0.1 and 3.7+-0.4, respectively. Based on these observations, there is no conclusive evidence for a nonterrestrial 16O/18O ratio.