  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.
