  We report measurements of the decays B+ -> Phi Phi K+ and B0 -> hi Phi K0
using a sample of 231 million BBbar pairs collected with the BABAR detector at
the PEP-II asymmetric-energy B Factory at the Stanford Linear Accelerator
Center. The branching fractions are measured to be Br(B+ -> Phi Phi K+) = (7.5
+/- 1.0 stat. +/- 0.7 syst.) * 10^-6 and Br(B0 -> Phi Phi K0) = (4.1 +1.7/-1.4
stat. +/- 0.4 syst.) * 10^-6 for a Phi Phi invariant mass below 2.85 GeV/c2.
