We have discovered heavy obscuration in the dual active galactic nucleus (AGN) in the Swift/Burst Alert Telescope (BAT) source SWIFT J2028.5+2543 using Nuclear Spectroscopic Telescope Array (NuSTAR). While an early XMM-Newton study suggested the emission was mainly from NGC 6921, the superior spatial resolution of NuSTAR above 10 keV resolves the Swift/BAT emission into two sources associated with the nearby galaxies MCG +04-48-002 and NGC 6921 (z = 0.014) with a projected separation of 25.3 kpc (91"). NuSTAR's sensitivity above 10 keV finds both are heavily obscured to Compton-thick levels (NH ~ (1–2) × 1024 cm-2) and contribute equally to the BAT detection (Lint10-50 keV ~ 6 × 1042 erg s-1). The observed luminosity of both sources is severely diminished in the 2–10 keV band (Lobs2-10 keV < 0.1 x Lint2-10 keV ), illustrating the importance of >10 keV surveys like those with NuSTAR and Swift/BAT. Compared to archival X-ray data, MCG +04-48-002 shows significant variability (>3) between observations. Despite being bright X-ray AGNs, they are difficult to detect using optical emission-line diagnostics because MCG +04-48-002 is identified as a starburst/composite because of the high rates of star formation from a luminous infrared galaxy while NGC 6921 is only classified as a LINER using line detection limits. SWIFT J2028.5+2543 is the first dual AGN resolved above 10 keV and is the second most heavily obscured dual AGN discovered to date in the X-rays other than NGC 6240
