We investigate the Ly \alpha and UV continuum morphology of one of the most luminous known Lyman \alpha emitting galaxies ( the ‘ Coup Fourré Galaxy ’ ) , associated with a z = 2.3 damped Ly \alpha absorption system in the spectrum of the QSO PHL 957 ( Lowenthal et al . 1991 ) . The galaxy is observed with the HST WFPC2 , through a narrow filter ( F410M ) corresponding to rest-frame Ly \alpha for a total exposure time of 41.2 ksec , plus shorter exposures in F555W and F814W . In all three passbands , the galaxy is resolved into a close ( \sim 0.35 arcsec ) pair of two components , CFgA and CFgB , both of which are extended and elongated . The profile of CFgA is consistent with an exponential disk of similar scale-length in Ly \alpha ( r _ { exp } = 0.23 arcsec ) and continuum ( r _ { exp } = 0.20 arcsec ) , and no evidence of a central point source . In contrast , CFgB is closer to a bulge profile . We find that CFgA has by far the higher ratio of Ly \alpha to continuum flux , and from the observed colours estimate rest-frame equivalent widths of W ( Ly \alpha ) = 151 \pm 16 \AA for CFgA and 33 \pm 13 \AA for CFgB . From the F814W and F555W magnitudes we estimate rest-frame blue-band absolute magnitudes ( for H _ { 0 } = 50 km s ^ { -1 } Mpc ^ { -1 } and q _ { 0 } = 0.05 ) of -23.12 for CFgA and -23.24 for CFgB , significantly brighter than local galaxies of the same size . CFgA shows a remarkable 3.9 magnitudes of surface brightness enhancement relative to local spirals . This object appears to be at the upper limit of both the range of surface brightness evolution observed in z > 2 galaxies and the range of W ( Ly \alpha ) in any star-forming galaxy . We speculate that its extreme surface brightness results from a very luminous starburst ( \sim 200 M _ { \odot } yr ^ { -1 } ) , triggered by the merger of the two components , and the high W ( Ly \alpha ) from a brief phase of the starburst in which most Ly \alpha photons can escape , as predicted in the models of Tenorio-Tagle et al . ( 1999 ) . We also investigate the F410M image of the QSO PHL 957 . Subtraction of a normalized point-spead function leaves no significant residuals – the QSO is consistent with a pure point source and we do not detect either the host galaxy or the damped Ly \alpha absorbing galaxy . We search for other galaxies with strong Ly \alpha emission at z \sim 2.3 –2.4 , selecting these by a colour ( m _ { 410 } - V _ { 555 } ) _ { AB } < -0.2 . Eight candidate Ly \alpha sources , all fainter than the Coup Fourré galaxy , are identified in our field . One is a point-source and may be an AGN ; the others are of similar size to the Coup Fourré Galaxy but lower surface brightness , knotty and asymmetric . They appear typical of Lyman break galaxies but with colours indicating W ( Ly \alpha ) \sim 100 \AA .