Measuring the response of the intergalactic medium to a blast of ionizing radiation allows one to infer the physical properties of the medium and, in principle, the lifetime and isotropy of the radiating source. The most sensitive such measurements can be made if the source of radiation is near the line of sight to a bright background QSO. We present results based on deep Keck/HIRES observations of the QSO triplet KP76, KP77 and KP78 at z ~2.5, with separations of 2-3 arcmin on the plane of the sky. Using accurate systemic redshifts of the QSOs from near-IR spectroscopy, we quantify the state of the IGM gas in the proximity regions where the expected ionizing flux from the foreground QSOs exceeds that of the metagalactic background by factors of 10-200, assuming constant and isotropic emission. Based on the unusual ionization properties of the absorption systems with detected HI, CIV, and OVI, we conclude that the gas has been significantly affected by the UV radiation from the nearby QSOs. Aided by observations of the galaxy density near the foreground QSOs, we discuss several effects that may explain why the transverse proximity effect has eluded most previous attempts to detect it. Our observations suggest that the luminosities of KP76 and KP77 have remained comparable to current values over timescales of, respectively, Delta t > 25 Myr and 16 Myr < Delta t < 33 Myr - consistent with typical QSO lifetimes estimated from independent, less-direct methods. There is no evidence that the UV radiation from either QSO was significantly anisotropic during these intervals.