We present a measurement of the average multiplicity of $ϕ$ mesons in $B^0$, $\kern 0.18em\bar{\kern -0.18em B}{}^0$ and $B^±$ meson decays. Using $17.6 fb^{-1}$ of data taken at the $\Upsilon{(4S)}\xspace$ resonance by the {\slshape B\kern-0.1em{\smaller A}\kern-0.1em B\kern-0.1em{\smaller A\kern-0.2em R}} detector at the PEP-II $e^+e^-\xspace$ storage ring at the Stanford Linear Accelerator Center, we reconstruct $ϕ$ mesons in the $K^+K^-$ decay mode and measure ${\cal{B}}(B\to ϕ X) = (3.41±0.06±0.12)%$. This is significantly more precise than any previous measurement. ; Comment: 9 pages, 4 figures, submitted to Phys. Rev. D