  We present the spectroscopic discovery of a broad-lined Type Ic supernova (SN
2010bh) associated with the nearby long-duration gamma-ray burst (GRB) 100316D.
At z = 0.0593, this is the third-nearest GRB-SN. Nightly optical spectra
obtained with the Magellan telescopes during the first week after explosion
reveal the gradual emergence of very broad spectral features superposed on a
blue continuum. The supernova features are typical of broad-lined SNe Ic and
are generally consistent with previous supernovae associated with low-redshift
GRBs. However, the inferred velocities of SN 2010bh at 21 days after explosion
are a factor of ~2 times larger than those of the prototypical SN 1998bw at
similar epochs, with v ~ 26,000 km/s, indicating a larger explosion energy or a
different ejecta structure. A near-infrared spectrum taken 13.8 days after
explosion shows no strong evidence for He I at 1.083 microns, implying that the
progenitor was largely stripped of its helium envelope. The host galaxy is of
low luminosity (M_R ~ -18.5 mag) and low metallicity (Z < 0.4 Z_solar), similar
to the hosts of other low-redshift GRB-SNe.
