The Breakthrough Listen search for intelligent life is, to date, the most extensive technosignature search of nearby celestial objects. We present a radio technosignature search of the centers of 97 nearby galaxies, observed by Breakthrough Listen at the Robert C. Byrd Green Bank Telescope. We performed a narrowband Doppler drift search using the turboSETI pipeline with a minimum signal-to-noise parameter threshold of 10, across a drift rate range of $\pm$ 4 Hz\ $s^{-1}$, with a spectral resolution of 3 Hz and a time resolution of $\sim$ 18.25 s. We removed radio frequency interference by using an on-source/off-source cadence pattern of six observations and discarding signals with Doppler drift rates of 0. We assess factors affecting the sensitivity of the Breakthrough Listen data reduction and search pipeline using signal injection and recovery techniques and apply new methods for the investigation of the RFI environment. We present results in four frequency bands covering 1 -- 11 GHz, and place constraints on the presence of transmitters with equivalent isotropic radiated power on the order of $10^{26}$ W, corresponding to the theoretical power consumption of Kardashev Type II civilizations.