Previous electron tunneling measurements1 on Ce in La showed that there were many more states at low energy than predicted by the Abrikosov-Gor'kov (AG) theory of gapless superconductivity. Further measurements on this system show that it is gapless even at very low concentrations and temperatures. This contrasts with the prediction of AG that there is an energy gap for n≤0.9ncr where n is the impurity concentration in at.% and ncr is the concentration which destroys superconductivity. At low impurity (Ce) concentrations in La the number of states in the gap N(0, 0) = (0.51±0.17)n. This result is most easily interpreted by assuming that one is observing a single impurity effect and that the energy gap is a function of position. Using this interpretation and the experimental results one finds the density of states has its normal state value for a range of approximately 7.6 Å around each impurity. It is possible that these added states are quasibound states formed near each Kondo impurity. © 1969 The American Institute of Physics.