  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
10e-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 3.4GeVc^2. A 90% confidence level upper limit of 6.4 x 10e-6 is
obtained for 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 10e6 B anti-B pairs collected at the Upsilon(4S) resonance with the Belle
detector at the KEKB asymmetric-energy e^+e^- collider.
