We have carried out a deep narrow-band imaging survey of six fields with heavy-element quasar absorption lines , using the Goddard Fabry-Perot ( FP ) system at the Apache Point Observatory ( APO ) 3.5-meter telescope . The aim of these observations was to search for redshifted Ly- \alpha emission from the galaxies underlying the absorbers at z = 2.3 - 2.5 and their companion galaxies . The 3 \sigma sensitivity levels ranged between 1.9 \times 10 ^ { -17 } and 5.4 \times 10 ^ { -17 } erg s ^ { -1 } cm ^ { -2 } in observed-frame Ly- \alpha flux . No significant Ly- \alpha emitters were detected at > 3 \sigma level . The absence of significant Ly- \alpha emission implies limits on the star formation rate ( SFR ) of 0.9-2.7 M _ { \odot } yr ^ { -1 } per 2-pixel x 2-pixel region , if no dust attenuation is assumed . We compare our results with those from other emission-line studies of absorber fields and with predictions for global average SFR based on the models of cosmic chemical evolution . Our limits are among the tightest existing constraints on Ly- \alpha emission from galaxies in absorber fields , but are consistent with many other studies . In the absence of dust attenuation , these studies suggest that SFRs in a large fraction of objects in the absorber fields may lie below the global mean SFR . However , it is possible that dust attenuation is responsible for the low emission line fluxes in some objects . It is also possible that the star-forming regions are compact and at smaller angular separations from the quasar than the width of our point spread function and , get lost in the quasar emission . We outline future observations that could help to distinguish between the various possibilities .