We report the discovery of a radio transient VLA 232937.2-235553, coincident with the proposed X-ray afterglow for the gamma-ray burst GRB 981226. This gamma-ray burst (GRB) has the highest ratio of X-ray to gamma-ray fluence of all the GRBs detected by BeppoSAX so far, and yet no corresponding optical transient was detected. The radio light curve of VLA 232937.2-235553 is qualitatively similar to that of several other radio afterglows. At the subarcsecond position provided by the radio detection, optical imaging reveals an extended R=24.9 mag object, which we identify as the host galaxy of GRB 981226. Afterglow models that invoke a jetlike geometry for the outflow or that require an ambient medium with a radial density dependence, such as that produced by a wind from a massive star, are both consistent with the radio data. Furthermore, we show that the observed properties of the radio afterglow can explain the absence of an optical transient without the need for large extinction local to the GRB.