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We present sensitive phase-referenced VLBI results on the radio continuumemission from the $z=4.4$ QSO BRI 1335--0417. The observations were carried outat 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 continuumemission 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 sourceat FWHM is $255 \times 138$ mas ($1.7 \times 0.9$ kpc) and the derivedintrinsic brightness temperature is $\sim 3.5\times 10^4$ K. No continuumemission 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 $\mu$Jybeam$^{-1}$, 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 ($0.35 \times0.18$ kpc). At this resolution, the image shows a continuum feature in BRI1335--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 ofthe observed continuum sources at 1.4 GHz and the derived brightnesstemperatures show that the radio emission (and thus presumably the far-infraredemission) in BRI 1335--0417 is powered by a major starburst, with a massivestar formation rate of order a few thousand M_{\odot} {\rm yr}^{-1}$. Moreover,the absence of any compact high-brightness temperature source suggests thatthere is no radio-loud AGN in this $z=4.4$ QSO.

High Sensitivity Array Observations of the $z = 4.4$ QSO BRI 1335-0417