Long-duration \gamma -ray bursts ( GRBs ) at z < 1 are in most cases found to be accompanied by bright , broad-lined Type Ic supernovae ( SNe Ic-BL ) . The highest-energy GRBs are mostly located at higher redshifts , where the associated SNe are hard to detect observationally . Here we present early and late observations of the optical counterpart of the very energetic GRB 130427A . Despite its moderate redshift z = 0.3399 \pm 0.0002 , GRB 130427A is at the high end of the GRB energy distribution , with an isotropic-equivalent energy release of E _ { iso } \sim 9.6 \times 10 ^ { 53 } erg , more than an order of magnitude more energetic than other GRBs with spectroscopically confirmed SNe . In our dense photometric monitoring , we detect excess flux in the host-subtracted r -band light curve , consistent with that expected from an emerging SN , \sim 0.2 mag fainter than the prototypical SN 1998bw . A spectrum obtained around the time of the SN peak ( 16.7 days after the GRB ) reveals broad undulations typical of SNe Ic-BL , confirming the presence of a SN , designated SN 2013cq . The spectral shape and early peak time are similar to those of the high expansion velocity SN 2010bh associated with GRB 100316D . Our findings demonstrate that high-energy long-duration GRBs , commonly detected at high redshift , can also be associated with SNe Ic-BL , pointing to a common progenitor mechanism .