We present a search for direct CP violation in B+/- --> J/psi K+/- and B+/-
--> psi(2S)K+/- decays. In a sample of 9.7 X 10(6) B (B) over bar meson pa
irs collected with the CLEO detector, we have fully reconstructed 534 B+/-
--> J/psi K+/- and 120 B+/- --> psi(2S)K+/- decays with very low background
. We have measured the CP-violating charge asymmetry to be [+1.8 +/- 4.3(st
at) +/- 0.4(syst)]% for B+/- --> J/psi K+/- and [+2.0 +/- 9.1(stat) +/- 1.0
(syst)]% for B+/- --> psi(2S)K+/-.