  We present preliminary results from a search for inclusive charmless B->KX
decays. These decays occur dominantly via one-loop b->s penguin transitions,
and can provide useful information about these processes. Using a sample of
288.5/fb collected with the BABAR detector at the PEP-II asymmetric-energy e+e-
B Factory at SLAC, we search for high-energy kaons recoiling against fully
reconstructed B decays. We measure the partial branching fractions for kaons
with momentum p*(K)>2.34GeV in the B rest frame, and obtain (in units of
10^-6): B(B->K+X, p*>2.34GeV) = 196^{+37}_{-34}(stat.)^{+31}_{-30}(syst.) and
B(B->K0X, p*>2.34GeV) = 154^{+55}_{-48}(stat.)^{+55}_{-41}(syst.) (<266 at 90%
C.L.).
