We present the results of a search for the radiative decay B -> K eta 'gamma and find evidence for B+ -> K+eta 'gamma decays at the 3.3 standard deviation level with a partial branching fraction of (3.6 +/- 1.2 +/- 0.4) x 10(-6), where the first error is statistical and the second systematic. This measurement is restricted to the region of combined K eta ' invariant mass less than 3.4 GeV/c(2). A 90% confidence level upper limit of 6.4 x 10(-6) is obtained for the partial branching fraction of the decay B-0 -> K-0 eta 'gamma in the same K eta ' invariant mass region. These results are obtained from a 605 fb(-1) data sample containing 657 x 10(6) B (B) over bar pairs collected at the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider.