We present the first measurement of the faint end of the QSO luminosity function at z = 3. The QSOs, which range from M sub(1450) =-21 to M sub(1450) =-27, were discovered in 17 fields totaling 0.43 deg super( 2) using multicolor selection criteria (the Lyman break technique) and spectroscopic follow-up. We find that the faint-end slope of the luminosity function is beta sub(l) = 1.24 plus or minus 0.07 ( phi proportional Limage), flatter than the value of beta sub(l) = 1.64 plus or minus 0.18 measured at lower redshift. The integrated rest 1450 Aa UV luminosity of z = 3 QSOs is only 50% of most previous estimates and only ~8% of that produced by Lyman break galaxies at the same redshifts. Assuming that ionizing photons from faint QSOs are as successful in escaping their host galaxies as bright QSOs, we estimate the total contribution of QSOs to the ionizing flux J sub(912) at z approx 3, J sub(912) ~ 2.4 x 10 super(-22) ergs s super(-1) cm super(-2) Hz super(-1). This estimate, which we regard as an upper limit, remains consistent with rough estimates of J sub(912) based on the Lyalpha forest "proximity effect."