  $B\to\chi_{c1}(1P,2P)K$ decays are studied in QCD factorization by treating
charmonia as nonrelativistic bound states. No infrared divergences exist in the
vertex corrections, while the logarithmic end-point singularities in the hard
spectator corrections can be regularized by a momentum cutoff. With certain
uncertainties we find that the $B\to\chi_{c1}(2P)K$ decay rate can be
comparable to $B\to\chi_{c1}(1P)K$, and get $Br(B^0 \to \chi_{c1}' K^0) =Br(B^+
\to \chi_{c1}' K^+)\approx 2\times 10^{-4}$. This might imply a possible
interpretation for the newly discovered X(3872) that this state has a dominant
$J^{PC} = 1^{++}(2P)$ $c\bar c$ component but mixed with a substantial
$D^0\bar{D}^{*0}+D^{*0}\bar{D}^0$ continuum component.
