Observing nearby galaxies would facilitate the search for artificial radio signals by sampling several billions of stars simultaneously, but few efforts have been made to exploit this opportunity. An added attraction is that the Milky Way is the second largest member of the Local Group, so our galaxy might be a probable target for hypothetical broadcasters in nearby galaxies. We present the first relatively high spectral resolution (<1 kHz) 21 cm band search for intelligent radio signals of complete galaxies in the Local Group with the Jansky VLA, observing the galaxies M31 (Andromeda) and M33 (Triangulum)-the first and third largest members of the group, respectively-sampling more stars than any prior search of this kind. We used 122 Hz channels over a 1 MHz spectral window in the target galaxy velocity frame of reference, and 15 Hz channels over a 125 kHz window in our local standard of rest. No narrowband signals were detected above a signal-to-noise ratio of 7, suggesting the absence of continuous narrowband flux greater than approximately 0.24 and 1.33 Jy in the respective spectral windows illuminating our part of the Milky Way during our observations in 2014 December and 2015 January. This is also the first study in which the upgraded VLA has been used for SETI.