Boyajian s Star (KIC 8462852) has received significant attention due to its unusual periodic brightness fluctuations detected by the Kepler Spacecraft and subsequent ground based observations. Possible explanations for the dips in the photometric measurements include interstellar or circumstellar dust, and it has been speculated that an artificial megastructure could be responsible. We analyze 177 high-resolution spectra of Boyajians Star in an effort to detect potential laser signals from extraterrestrial civilizations. The spectra were obtained by the Lick Observatorys Automated Planet Finder telescope as part of the Breakthrough Listen Project, and cover the wavelength range of visible light from 374 to 970 nm. We calculate that the APF would be capable of detecting lasers of power greater than approximately 24 MW at the distance of Boyajians Star, d = 1470 ly. The top candidates from the analysis can all be explained as either cosmic ray hits, stellar emission lines or atmospheric air glow emission lines.