The existence of binary supermassive black holes (SBHs) is predicted by models of hierarchical galaxy formation. To date, only a single binary SBH has been imaged, at a projected separation of 7.3 parsecs. Here we report the detection of a candidate dual SBH with projected separation of 0.35 pc in the gas-rich interacting spiral galaxy NGC 7674 (Mrk 533). This peculiar Seyfert galaxy possesses a $sim$0.7 kpc Z-shaped radio jet; the leading model for the formation of such sources postulates the presence of an uncoalesced binary SBH created during the infall of a satellite galaxy. Using very long baseline interferometry (VLBI), we imaged the central region of Mrk 533 at radio frequencies of 2, 5, 8 and 15 GHz. Two, possibly inverted-spectrum radio cores were detected at 15 GHz only; the 8-15 GHz spectral indices of the two cores are $ge-0.33$ and $ge-0.38$ ($pm 30%$), consistent with accreting SBHs. We derive a jet speed $sim0.28c$ from multi-epoch parsec-scale data of the hotspot region, and a source age $ge8.2times10^3$ yrs.
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