  We have searched for the two-body decay of the B meson to a light
pseudoscalar meson $h = \pi^+, K^+, K^0_S$ and a massless neutral
weakly-interacting particle $X^0$ such as the familon, the Nambu-Goldstone
boson associated with a spontaneously broken global family symmetry. We find no
significant signal by analyzing a data sample containing 9.7 million $B\bar{B}$
mesons collected with the CLEO detector at the Cornell Electron Storage Ring,
and set a 90% C.L. upper limit of $4.9 \times 10^{-5}$ and $5.3 \times 10^{-5}$
on the branching fraction for the decays $B^+ \to h^+ X^0$ and $B^0 \to K^0_S
X^0$, respectively. These upper limits correspond to a lower bound of about
$10^{8}$ GeV on the family symmetry breaking scale involving the third
generation of quarks.
