We present quantum Monte Carlo calculations of the single- and two-nucleon momentum distributions in selected nuclei for A <= 16. We employ local chiral interactions at next-to-next-to-leading order. We find good agreement at low momentum with the single-nucleon momentum distributions derived for phenomenological potentials. The same agreement is found for the integrated two-nucleon momentum distributions at low relative momentum q and low center-of-mass momentum Q. We provide results for the two-nucleon momentum distributions as a function of both q and Q. The large ratio of pn to pp pairs around q = 2 fm(-1) for back-to-back (Q = 0) pairs is confirmed up to O-16, and results are compatible with those extracted from available experimental data.