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 ^ { \prime \prime } \times 0.34 ^ { \prime \prime } ( 3.9 \times 2.9 kpc ) resolution shows a marginally resolved continuum structure with a peak flux density of 148 \pm 38 ~ { } \mu Jy beam ^ { -1 } , and a total flux density of 168 \pm 73 ~ { } \mu Jy , consistent with previous VLA and MERLIN measurements . The deconvolved size of the source is 0 \hbox to 0.0 pt { . } { { } ^ { \prime \prime } } 27 ( \pm 0 \hbox to 0.0 pt { . } { { } ^ { \prime% \prime } } 12 ) \times < 0 \hbox to 0.0 pt { . } { { } ^ { \prime \prime } } 23 , or 2.3 ( \pm 1.0 ) \times < 1.9 kpc { { } ^ { 2 } } , and the derived intrinsic brightness temperature is > ( 5 \pm 2 ) \times 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 \times 7.2 mas , 111 \times 61 pc ) , with a 4 \sigma point source upper limit of 26 \mu Jy beam ^ { -1 } , or an upper limit to the intrinsic brightness temperature of 4.7 \times 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 \sim 2500 M _ { \odot } ~ { } { yr } ^ { -1 } . 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 .