  We report on a measurement of the decay $K_L\rightarrow\mu^+\mu^-\gamma$ from
Fermilab experiment E799. We observe $207$ candidate signal events with an
estimated background of $10.5 \pm 4.0$ events and establish
$B(K_L\rightarrow\mu^+\mu^-\gamma) = (3.23\pm 0.23(stat) \pm 0.19(sys))\times
10^{-7}$. This provides the first measurement of the $K\gamma\gamma^*$ form
factor in the muonic Dalitz decay mode of the $K_L$.
