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We construct a chemical model for the envelope of SN 1987A at day 192. It is found that the $H$ and $He$ ionization fractions are quite low and a significant amount of $H_2$ is formed. The $H_3^+$ density is about $10^{-8}n_H$. The dominant $H_3^+$ excitation mechanism is atomic hydrogen impact excitation. The $H_3^+$ vibrational population falls short of LTE, and we are able to use the $H_3^+$ spectrum to fit the observed $3-4\mu m$ spectrum of SN 1987A at day 192 quite well. Cooling is mainly through the $OH$ rotational cooling. The temperature in the envelope at day 192 is probably between 1000 and $2000K$. We conclude that interstellar $H_3^+$ has been found.
