  The results of a search for $W$ boson pair production in $p\bar{p}$
collisions at $\sqrt{s}=1.8$ TeV with subsequent decay to dilepton ($e\mu, ee
$, and $\mu\mu$) channels are presented. One event is observed with an expected
background of $0.56\pm0.13$ events with an integrated luminosity of
approximately 14 pb$^{-1}$. %$13.9\pm1.7$ pb$^{-1}$. Assuming equal strengths
for the $WWZ$ and $WW\gamma$ gauge boson coupling parameters $\kappa$ and
$\lambda$, limits on the CP-conserving anomalous coupling constants are
$-2.6<\Delta\kappa<2.8$ and $-2.2<\lambda<2.2$ at the 95% confidence level.
