We search for the factorization-suppressed decays B-->chi(c0)K(*) and B-->chi(c2)K(*), with chi(c0) and chi(c2) decaying into J/psi gamma, using a sample of 124 x 10(6) BB events collected with the BABAR detector at the PEP-II storage ring of the Stanford Linear Accelerator Center. We find no significant signal and set upper bounds for the branching fractions.