  The lack of success of Lyman-alpha searches for high-redshift (z>2) field
galaxies may be due to extinction by dust, suggesting that surveys based on
lines of longer wavelength, particularly H-alpha, may be more effective. To
test the dust hypothesis we have undertaken deep broad- (K') and narrow-band
(5000 km/s, 2.177 micron) imaging of the field towards the quasar PHL957, in an
attempt to detect H-alpha emission from a known galaxy of redshift z=2.313. We
cover an area of 4.9 square arcmin (0.28 h^{-2}Mpc^2) to a 4-sigma limiting
narrow-band flux f=2.7x10^{-16}erg/s/cm^2, a factor of several deeper than
previously published surveys. We detect the H-alpha+[N II] emission line in
this galaxy at the 3.3-sigma level, inferring a star formation rate of 18
h^{-2} solar masses per year. This is a factor only a few times larger than the
rate seen in some Sc galaxies today. The faint flux level reached in this work
demonstrates the promise of narrow-band imaging in the near-infrared as a
technique for finding normal galaxies at high redshifts.
