We present the discovery and follow-up observations of a broad-line type-Ic supernova ( SN ) , PTF 10bzf ( SN 2010ah ) , detected by the Palomar Transient Factory ( PTF ) on 2010 February 23 . The SN distance is \cong 218 Mpc , greater than GRB 980425 / SN 1998bw and GRB 060218 / SN 2006aj , but smaller than the other SNe firmly associated with gamma-ray bursts ( GRBs ) . We conducted a multi-wavelength follow-up campaign with Palomar-48 inch , Palomar 60-inch , Gemini-N , Keck , Wise , Swift , the Allen Telescope Array , CARMA , WSRT , and EVLA . Here we compare the properties of PTF 10bzf with those of SN 1998bw and other broad-line SNe . The optical luminosity and spectral properties of PTF 10bzf suggest that this SN is intermediate , in kinetic energy and amount of ^ { 56 } Ni , between non GRB-associated SNe like 2002ap or 1997ef , and GRB-associated SNe like 1998bw . No X-ray or radio counterpart to PTF 10bzf was detected . X-ray upper-limits allow us to exclude the presence of an underlying X-ray afterglow as luminous as that of other SN-associated GRBs like GRB 030329 or GRB 031203 . Early-time radio upper-limits do not show evidence for mildly-relativistic ejecta . Late-time radio upper-limits rule out the presence of an underlying off-axis GRB , with energy and wind density similar to the SN-associated GRB 030329 and GRB 031203 . Finally , by performing a search for a GRB in the time window and at the position of PTF 10bzf , we find that no GRB in the IPN catalog could be associated with this SN .