We discuss a sample of 29 AGN (16 narrow-lined and 13 broad-lined) discovered in a spectroscopic survey of ~1000 star-forming Lyman-break galaxies (LBGs) at z~3. Reaching apparent magnitudes of R_{AB}=25.5, the sample includes broad-lined AGN approximately 100 times less UV-luminous than most surveys to date covering similar redshifts, and the first statistical sample of UV/optically-selected narrow-lined AGN at high redshift. The fraction of objects in our survey with clear evidence for AGN activity is ~3%. A substantial fraction, perhaps even most, of these objects would not have been detected in even the deepest existing X-ray surveys. We argue that these AGN are plausibly hosted by the equivalent of LBGs. The UV luminosities of the broad-lined AGN in the sample are compatible with Eddington-limited accretion onto black holes that satisfy the locally determined M_{BH} versus M_{bulge} relation given estimates of the stellar masses of LBGs. The clustering properties of the AGN are compatible with their being hosted by objects similar to LBGs. The implied lifetime of the active AGN phase in LBGs, if it occurs some time during the active star-formation phase, is ~10^7 years.
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