We report a search for the rare charmless decay B+ -> (K) over bar*K-0*(+) using a data sample of 772 x 10(6) B (B) over bar pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. No statistically significant signal is found and a 90% confidence- level upper limit is set on the decay branching fraction of B(B+ -> (K) over bar*K-0*(+)) < 1.31 x 10(-6).