Measurements are reported of the cross section for the non-symmetric charge transfer /sup 3/He/sup 2+/+H* rarr /sup 3 /He/sup +/+H/sup +/ in the relative energy range 0.25 to 478 eV for excited hydrogen atoms with principal quantum numbers /b n/ ranging from 8 to 24. The experimental method involves merged beams and time-correlation analysis of the reaction products. Field ionisation is used to modify and specify the population of the excited states. The results are presented as cross sections sigma (/b n//sub 1/, /b n//sub 2/) averaged over consecutive values of /b n/ ranging from /b n//sub 1/ to /b n //sub 2/, namely sigma (8, 9), sigma (10, 14), sigma (15, 19) and sigma (20, 24). The cross sections are large, up to 10/sup -10/ cm/sup 2/, and appear to be roughly independent of energy below 50 eV.