We have measured the branching fractions for the exclusive decay modes B -> chi(c1(2)) K(K*) using a 140 fb(-1) data sample collected by the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. The measured branching fractions for B+ -> chi(c1) K+, B-0, chi(c1) K-0, B-0 -> chi(c1) K*(0) and B+ -> chi(c1) K*(+) decay modes are (4.5 +/- 0.2 +/- 0.5) x 10(-4), (3.5 +/- 0.3 +/- 0.5) x 10(-4), (3.1 +/- 0.3 +/- 0.7) x 10(-4) and (4.1 +/- 0.6 +/- 0.9) x 10(-4), respectively, where the first error is statistical and the second error is systematic. We do not observe statistically significant signals for the B -> chi(c2) K(K*) decay modes and set upper limits at the 90% confidence level. We also study the helicity distribution for B -> chi(c1) K* decay mode and show that the longitudinal polarization component is dominant. (c) 2006 Elsevier B.V. All rights reserved.