We present sensitive phase-referenced VLBI results on the radio continuum emission from the z=1.87 luminous submillimeter galaxy (SMG) GOODS 850-3. The observations were carried out at 1.4 GHz using the High Sensitivity Array (HSA). Our sensitive tapered VLBI image of GOODS 850-3 at 0.47 x 0.34 arcsec (3.9 x 2.9 kpc) resolution shows a marginally resolved continuum structure with a peak flux density of 148 pm 38 uJy/beam, and a total flux density of 168 pm 73 uJy, consistent with previous VLA and MERLIN measurements. The derived intrinsic brightness temperature is > 5 pm 2 x 10^3 K. The radio continuum position of this galaxy coincides with a bright and extended near-infrared source that nearly disappears in the deep HST optical image, indicating a dusty source of nearly 9 kpc in diameter. No continuum emission is detected at the full VLBI resolution (13.2 x 7.2 mas, 111 x 61 pc), with a 4-sigma point source upper limit of 26 uJy/beam, or an upper limit to the intrinsic brightness temperature of 4.7 x 10^5 K. The extent of the observed continuum source at 1.4 GHz and the derived brightness temperature limits are consistent with the radio emission (and thus presumably the far-infrared emission) being powered by a major starburst in GOODS 850-3, with a star formation rate of ~2500 M_sun/yr. Moreover, the absence of any continuum emission at the full resolution of the VLBI observations indicates the lack of a compact radio AGN source in this z=1.87 SMG.
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