HUBBLE-SPACE-TELESCOPE IMAGING OF A RADIO-QUIET GALAXY AT REDSHIFT Z=3.4

We have observed with the Wide Field/Planetary Camera (WF/PC) on the H ubble Space Telescope (HST) a radio-quiet Lyalpha-emitting galaxy at r edshift z = 3.428 (G2 below). The images probe the rest-frame UV light around 1250 angstrom with an angular resolution of almost-equal-to 0' '.1, corresponding to 1.4 h50(-1) kpc at redshift z = 3.4 (in this Let ter we use q0 = 0 and H0 = 50 h50(-1) km s-1 Mpc-1). The light profile of the central approximately 10 h50(-1) kpc region is well fitted by an r1/4 law with r(e) almost-equal-to 1.3 h50(-1) kpc, suggesting a dy namically relaxed state. The outer regions are characterized by the pr esence of substructures, such as an elongated formation and low surfac e brightness nebulosities. The isophotal analysis shows no evidence of an AGN-like unresolved source in the center. The structural propertie s of G2 are consistent with a dynamically hot stellar system observed during an early phase of star formation, very likely the progenitor of an elliptical or the bulge of a spiral galaxy.