We have used the Very Large Array to observe the nearby spiral galaxy NGC 7331. The observations detected an unresolved radio source in the nucleus of this galaxy, with flux densities of 234 +/- 25 mu Jy and 121 +/- 16 mu Jy at 20 and 6 cm, respectively. This is equivalent (at the distance of this galaxy) to luminosities of approximately 3 and 4 times that of the Galactic center source Sgr A at 20 and 6 cm. The source in NGC 7331, with a radio spectral index (S-mu proportional to mu(alpha)) of alpha = -0.6 +/- 0.1, sits in a region of very low gas density, surrounded by a ring of radio emission. Optical spectra show that NGC 7331 has a weak LINER nucleus. We compare the radio and optical properties of this nucleus with other LINER nuclei detected in the radio, and find that NGC 7331 has an unusually low radio to H alpha flux ratio. The combination of an unresolved radio source and a LINER nucleus spectrum suggests that this galaxy harbors a massive black hole. The radio observations of NGC 7331 did not detect emission from the historical supernova 1959D with a 3 sigma upper limit of 75 mu Jy at 20 cm.