Recoil-isomer tagging with the (54)Fe + (92)Mo reaction was used to establish a 10(2)-mu s isomeric state in (139)Eu. Prompt versus delayed gamma-ray coincidence data have revealed the presence of a prompt rotational band built upon the isomer. The alignment properties of the states in this band show that the isomer is based upon a proton g(7/2) configuration. The decay of the isomer takes place through a single 26-keV E1 transition. The gamma-ray transition strength for this decay is consistent with those established in the neighboring isomeric gamma-soft nuclei. In these nuclei, isomers are expected to form as a consequence of differences in nuclear shapes or configurations, and the natural hindrance associated with configuration-changing E1 transitions. The isomeric nature of the state in (139)Eu is reasoned to be because of difference in shape of the proton g(7/2) state and the proton h(11/2) ground state to which it decays.