We estimate the star formation efficiency per gravitational free-fall time, , from observations of nearby galaxies with resolution matched to the typical size of a giant molecular cloud. This quantity, , is theoretically important but so far has only been measured for Milky Way clouds or inferred indirectly in a few other galaxies. Using new, high-resolution CO imaging from the Physics at High Angular Resolution in nearby Galaxies-Atacama Large Millimeter Array (PHANGS-ALMA) survey, we estimate the gravitational free-fall time at 60-120 pc resolution, and contrast this with the local molecular gas depletion time in order to estimate . Assuming a constant thickness of the molecular gas layer (H = 100 pc) across the whole sample, the median value of in our sample is 0.7%. We find a mild scale dependence, with higher measured at coarser resolution. Individual galaxies show different values of , with the median ranging from 0.3% to 2.6%. We find the highest in our lowest-mass targets, reflecting both long free-fall times and short depletion times, though we caution that both measurements are subject to biases in low-mass galaxies. We estimate the key systematic uncertainties, and show the dominant uncertainty to be the estimated line-of-sight (LOS) depth through the molecular gas layer and the choice of star formation tracers.