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The question whether the stellar initial mass function (IMF) is universal or varies with galactic environment is one of the most vexing in all of astrophysics. In the past decade there has been a particular focus on the centers of massive early-type galaxies comma as studies of gravity-sensitive absorption lines and kinematics have found evidence for an excess of low mass stars in these regions compared to the IMF of the Milky Way. We propose to test this hypothesis by measuring the average chromospheric activity of stars in the centers of 22 dust-free early-type galaxies spanning a wide range of masses comma ages comma abundances comma and spectroscopically-derived IMFs. The chromospheres of M dwarfs are very active comma as has been well-established in the context of the habitability of orbiting planets comma and the average level of activity in a stellar population is a strong function of the prevalence of these stars. The dominant chromospheric emission line is Ly-alpha comma which we can measure using the G130M grating of COS. If the IMF varies from galaxy to galaxy we expect to see a correlation between the strength of Ly-alpha and the strength of gravity-sensitive absorption features. The program uses the same instrumental setup as was used for observations of two early-type galaxies in Cycle 27 comma and an analysis of those observations shows that the measurements are feasible. The proposed spectra will have substantial long-term value beyond this primary aim. The Cycle 27 data appear to be the highest quality far-UV spectra of early-type galaxies ever taken comma and the full sample will constitute a legacy spectroscopic dataset of HST that complements the many orbits of archival imaging of these galaxies.