  We report the observation of $\e^+e^-\to \phi\eta$ near $\sqrt{s}$ = 10.58
GeV with 6.5 $\sigma$ significance in the $K^+K^-\gamma\gamma$ final state in a
data sample of 224 $fb^{-1}$ collected by the BaBar experiment at the PEP-II
$e^+e^-$ storage rings. We measure the restricted radiation-corrected cross
section to be $\sigma(\e^+e^- \to \phi \eta) =$$2.1\pm 0.4 (\mathrm{stat})\pm
0.1(\mathrm{syst}) \mathrm{fb}$ within the range $|\cos\theta^*| < 0.8$, where
$\theta^*$ is the center-of-mass polar angle of the $\phi$ meson. The $\phi$
meson is required to be in the invariant mass range of 1.008 $< m_{\phi} <$
1.035 \gevcc. The radiation-corrected cross section in the full $\cos\theta^*$
range is extrapolated to be $2.9\pm 0.5 (\mathrm{stat})\pm 0.1(\mathrm{syst})
\mathrm{fb}$.
