  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 $\ge8.2\times10^3$ yrs.
