  We have measured the branching fractions for the exclusive decay modes $B\to
{\chi}_{c1(2)} K(K^*)$ using a $140~{\rm fb}^{-1}$ data sample collected by the
Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. The measured
branching fractions for $B^+\to {\chi}_{c1}K^+$, $B^0\to {\chi}_{c1}K^0$,
$B^0\to {\chi}_{c1}K^{*0}$ and $B^+\to {\chi}_{c1}K^{*+}$ decay modes are
$(4.5\pm 0.2\pm0.5)\times 10^{-4}$, $(3.5\pm 0.3\pm0.5)\times 10^{-4}$,
$(3.1\pm 0.3\pm0.7)\times 10^{-4}$ and $(4.1\pm 0.6\pm0.9)\times 10^{-4}$,
respectively, where the first error is statistical and the second error is
systematic. We do not observe statistically significant signals for the $B\to
{\chi}_{c2}K(K^*)$ decay modes and set upper limits at the 90% confidence
level. We also study the helicity distribution for $B\to {\chi}_{c1} K^*$ decay
mode and show that the longitudinal polarization component is dominant. {{\it
Keywords:} {$B$-meson, Charmonium, Branching Fractions, Polarization}} {{\it
PACS:} 13.25.Hw, 11.30.Er}
