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The observations of CO and SiO in the infrared spectrum of SN1987A clearly indicate that molecules can form in the debris of a supernova explosion. Since ${\rm H}_2$ is not easily observable we compute its abundance theoretically. For conditions typical of the inner ($v < 2500 {\rm km s}^{-1}$) envelope of SN1987A, the fraction of H that is in molecular form rises to $\sim 1\%$ by $t \sim 800$ d. For $t < 500$ d the formation is dominated by the gas phase reactions ${\rm H} + {\rm H}^+ \rightarrow {\rm H}_2^+ + {\rm h} \nu$; ${\rm H}_2^+ + {\rm H} \rightarrow {\rm H}_2 + {\rm H}^+$. Thereafter, the formation is dominated by the reactions ${\rm H} + {\rm e} \rightarrow {\rm H}^- + {\rm h} \nu$; ${\rm H}^- + {\rm H} \rightarrow {\rm H}_2 + {\rm e}$. At early times the ${\rm H}^-$ may absorb $\sim 10-30\%$ of visible photons, contributing to the apparent paucity of ${\rm H} \alpha$ emission. For $t > 800$ d the abundance of ${\rm H}_2$ ``freezes out'' due to the slowing of all reactions. The opacity of the supernova envelope in the range $912 < \lambda < 1150$ \AA\ is dominated by resonance scattering in the Lyman and Werner bands of ${\rm H}_2$. The resulting fluorescence emission bands of ${\rm H}_2$ in the range $1150 < \lambda < 1650$ \AA\ may be observable in the UV spectra of supernovae at late times.
