Since the discovery of the first short-population γ-ray burst (GRB) afterglows in 2005, the handful of observed events have been found to be embedded in nearby (z < 1), bright underlying galaxies. We present multiwavelength observations of GRB 060121, the first short burst observed to clearly outshine its host galaxy (by a factor >102). A photometric redshift for this event places the progenitor at a most probable redshift of z = 4.6, with a less probable scenario of z = 1.7. In either case, GRB 060121 could be the farthermost short-population GRB detected to date and implies an isotropic-equivalent energy release in gamma rays comparable to that seen in long-population bursts. We discuss the implications of the released energy on the nature of the progenitor. These results suggest that GRB 060121 may belong to a family of energetic short-population events, lying at z > 1 and whose optical afterglows would outshine their host galaxies, unlike the first short GRBs observed in 2005. The possibility of GRB 060121 being an intermediate-duration burst is also discussed.