This paper tests for and measures monopsony power in the U.S. higher education labor market. It does so by directly estimating the residual labor supply curves facing individual four-year colleges and universities using school-specific labor demand instruments. The results indicate that schools have significant monopsony power over their tenure track faculty. Its magnitude is monotonic in rank, being greatest over full professors and smaller for associate and assistant professors. For non-tenure track faculty, however, universities do not seem to have any monopsony power and instead face perfectly elastic residual labor supply curves. Universities' market power over tenure track faculty does not differ between public and private schools nor between female and male faculty. Monopsony power is greater for larger universities, and the geographic market for faculty seems to be national rather than local. Monopsony power is also larger at higher-status institutions as measured by Carnegie classifications, average test scores of the undergraduate student body, or initial salary rankings. The results also suggest that monopsony power has contributed to the trend toward non-tenure track faculty in U.S. [The Initiative on Global Markets at the University of Chicago's Booth School provided financial assistance.]