  CXO J133815.6+043255 is an ultraluminous X-ray source (ULX) with ultraviolet,
optical, and radio counterparts located 10 kpc away from the nucleus of the
galaxy NGC 5252. Optical spectroscopic studies indicate that the ULX is
kinematically associated with NGC 5252; yet, the compactness of its radio
emission could not rule out the possibility that the ULX is a background
blazar. We present follow-up VLBA radio observations that are able to resolve
the compact radio emission of the ULX into two components, making the blazar
scenario very unlikely. The east component is extended at 4.4 GHz and its
detection also at 7.6 GHz reveals a steep spectral index. The west component is
only detected at 4.4 GHz, is not firmly resolved, and has a flatter spectral
index. Considering that the west component hosts the radio core, we constrain
the black hole mass of the ULX to $10^{3.5} < M_\mathrm{BH} \lesssim 2 \times
10^{6}$ M$_{\odot}$ and its Eddington ratio to $\sim 10^{-3}$. The ULX is thus
most likely powered by an intermediate-mass black hole or low-mass AGN. Our
results constitute the first discovery of a multi-component radio jet in a ULX
and possible intermediate-mass black hole.
