We have measured the K-shell internal conversion coefficient, alpha-K, for the 65.7-keV M4 transition in 119Sn to be 1621(25). This result agrees well with Dirac-Fock calculations in which the effect of the K-shell atomic vacancy is accounted for, and disagrees with calculations in which the vacancy is ignored. This extends our precision tests of theory to Z = 50, the lowest Z yet measured.