  We present Hubble Space Telescope (HST) observations of the exceptionally
bright and luminous Swift gamma-ray burst, GRB 130427A. At z=0.34 this burst
affords an excellent opportunity to study the supernova and host galaxy
associated with an intrinsically extremely luminous burst ($E_{iso} >10^{54}$
erg): more luminous than any previous GRB with a spectroscopically associated
supernova. We use the combination of the image quality, UV capability and and
invariant PSF of HST to provide the best possible separation of the afterglow,
host and supernova contributions to the observed light ~17 rest-frame days
after the burst utilising a host subtraction spectrum obtained 1 year later.
Advanced Camera for Surveys (ACS) grism observations show that the associated
supernova, SN~2013cq, has an overall spectral shape and luminosity similar to
SN 1998bw (with a photospheric velocity, v$_{ph}$ ~15,000 km/s). The positions
of the bluer features are better matched by the higher velocity SN~2010bh
(v$_{ph}$ ~ 30,000 km/s), but SN 2010bh is significantly fainter, and fails to
reproduce the overall spectral shape, perhaps indicative of velocity structure
in the ejecta. We find that the burst originated ~4 kpc from the nucleus of a
moderately star forming (1 Msol/yr), possibly interacting disc galaxy. The
absolute magnitude, physical size and morphology of this galaxy, as well as the
location of the GRB within it are also strikingly similar to those of
GRB980425/SN 1998bw. The similarity of supernovae and environment from both the
most luminous and least luminous GRBs suggests broadly similar progenitor stars
can create GRBs across six orders of magnitude in isotropic energy.
