We have discovered heavy obscuration in the dual active galactic nucleus ( AGN ) in the Swift /BAT source SWIFT J2028.5 + 2543 using 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 ^ { \prime \prime } ) . NuSTAR ’ s sensitivity above 10 keV finds both are heavily obscured to Compton-thick ( N _ { H } \approx 1 - 2 \times 10 ^ { 24 } cm ^ { -2 } ) and contribute equally to the BAT detection ( L _ { 10 - 50 keV } ^ { int } \approx 6 \times 10 ^ { 42 } { \thinspace erg } { \thinspace s } ^ { -1 } ) . The observed luminosity of both sources is severely diminished in the 2-10 keV band ( L _ { 2 - 10 keV } ^ { obs } < 0.1 \times L _ { 2 - 10 keV } ^ { int } ) , 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 detected AGN , both 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 2nd most heavily obscured dual AGN discovered to date in the X-rays other than NGC 6240 .