  Spectra of broad-lined Type Ic supernovae (SN Ic-BL), the only kind of SN
observed at the locations of long-duration gamma-ray bursts (LGRBs), exhibit
wide features indicative of high ejecta velocities (~0.1c). We study the host
galaxies of a sample of 245 low-redshift (z<0.2) core-collapse SN, including 17
SN Ic-BL, discovered by galaxy-untargeted searches, and 15 optically luminous
and dust-obscured z<1.2 LGRBs. We show that, in comparison with SDSS galaxies
having similar stellar masses, the hosts of low-redshift SN Ic-BL and z<1.2
LGRBs have high stellar-mass and star-formation-rate densities. Core-collapse
SN having typical ejecta velocities, in contrast, show no preference for such
galaxies. Moreover, we find that the hosts of SN Ic-BL, unlike those of SN
Ib/Ic and SN II, exhibit high gas velocity dispersions for their stellar
masses. The patterns likely reflect variations among star-forming environments,
and suggest that LGRBs can be used as probes of conditions in high-redshift
galaxies. They may be caused by efficient formation of massive binary
progenitors systems in densely star-forming regions, or, less probably, a
higher fraction of stars created with the initial masses required for a SN
Ic-BL or LGRB. Finally, we show that the preference of SN Ic-BL and LGRBs for
galaxies with high stellar-mass and star-formation-rate densities cannot be
attributed to a preference for low metal abundances but must reflect the
influence of a separate environmental factor.
