The radio-emitting quasar SDSS J1425+3231 (z=0.478) was recently found to have double-peaked narrow [O III] optical emission lines. Based on the analysis of the optical spectrum, Peng et al. (2011) suggested that this object harbours a dual active galactic nucleus (AGN) system, with two supermassive black holes (SMBHs) separated on the kpc scale. SMBH pairs should be ubiquitous according to hierarchical galaxy formation scenarios in which the host galaxies and their central black holes grow together via interactions and eventual mergers. Yet the number of presently-confirmed dual SMBHs on kpc or smaller scales remains small. A possible way to obtain direct observational evidence for duality is to conduct high-resolution radio interferometric measurements, provided that both AGN are in an evolutionary phase when some activity is going on in the radio. We used the technique of Very Long Baseline Interferometry (VLBI) to image SDSS J1425+3231. Observations made with the European VLBI Network (EVN) at 1.7 GHz and 5 GHz frequencies in 2011 revealed compact radio emission at sub-mJy flux density levels from two components with a projected linear separation of \sim2.6 kpc. These two components support the possibility of a dual AGN system. The weaker component remained undetected at 5 GHz, due to its steep radio spectrum. Further study will be necessary to securely rule out a jet--shock interpretation of the less dominant compact radio source. Assuming the dual AGN interpretation, we discuss black hole masses, luminosities, and accretion rates of the two components, using available X-ray, optical, and radio data. While high-resolution radio interferometric imaging is not an efficient technique to search blindly for dual AGN, it is an invaluable tool to confirm the existence of selected candidates.