We present sensitive phase-referenced VLBI results on the radio continuum emission from the z = 4.4 QSO BRI 1335–0417 . The observations were carried out at 1.4 GHz using the High Sensitivity Array ( HSA ) . Our sensitive VLBI image at 189 \times 113 mas ( 1.25 \times 0.75 kpc ) resolution shows continuum emission in BRI 1335–0417 with a total flux density of 208 \pm 46 ~ { } \mu Jy , consistent with the flux density measured with the VLA . The size of the source at FWHM is 255 \times 138 mas ( 1.7 \times 0.9 kpc ) and the derived intrinsic brightness temperature is \sim 3.5 \times 10 ^ { 4 } K. No continuum emission is detected at the full VLBI resolution ( 32 \times 7 mas , 211 \times 46 pc ) , with a 4 \sigma point source upper limit of 34 \mu Jy beam ^ { -1 } , or an upper limit to the intrinsic brightness temperature of 5.6 \times 10 ^ { 5 } K. The highest angular resolution with at least a 4.5 \sigma detection of the radio continuum emission is 53 \times 27 mas ( 0.35 \times 0.18 kpc ) . At this resolution , the image shows a continuum feature in BRI 1335–0417 with a size of 64 \times 35 mas ( 0.42 \times 0.23 kpc ) at FWHM , and intrinsic brightness temperature of \sim 2 \times 10 ^ { 5 } K. The extent of the observed continuum sources at 1.4 GHz and the derived brightness temperatures show that the radio emission ( and thus presumably the far-infrared emission ) in BRI 1335–0417 is powered by a major starburst , with a massive star formation rate of order a few thousand M _ { \odot } ~ { } { yr } ^ { -1 } . Moreover , the absence of any compact high-brightness temperature source suggests that there is no radio-loud AGN in this z = 4.4 QSO .