We present late-time radio observations of 68 local Type Ibc supernovae, including six events with broad optical absorption lines ("hypernovae"). None of these objects exhibit radio emission attributable to off-axis gamma-ray burst jets spreading into our line of sight. Comparison with our afterglow models reveals the following conclusions. (1) Less than ~10% of Type Ibc supernovae are associated with typical gamma-ray bursts initially directed away from our line of sight; this places an empirical constraint on the GRB beaming factor of f 104, corresponding to an average jet opening angle, θj 08. (2) This holds in particular for the broad-lined supernovae (SNe 1997dq, 1997ef, 1998ey, 2002ap, 2002bl, and 2003jd), which have been argued to host GRB jets. Our observations reveal no evidence for typical (or even subenergetic) GRBs and rule out the scenario in which every broad-lined SN harbors a GRB at the 84% confidence level. Their large photospheric velocities and asymmetric ejecta (inferred from spectropolarimetry and nebular spectroscopy) appear to be characteristic of the nonrelativistic SN explosion and do not necessarily imply the existence of associated GRB jets.
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