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We present the discovery of a low-redshift damped Ly$α$ (DLA) system in the spectrum of background starburst galaxy SDSS J111323.88+293039.3 ($z=0.17514$). The DLA is at an impact parameter of $\rm ρ=36~kpc$ from the star forming galaxy, SDSS J111324.08+293051.2 ($z=0.17077$). We measure an HI column density of $N($HI$)\rm =3.47\times10^{20}~cm^{-2}$ along with multiple low-ionization species such as NI, NII, SiII, CII, and SiIII. We also make an estimate of the covering fraction to be 0.883, giving us a limiting size of the DLA to be $A_{DLA}\rm \geq3.3~kpc^2$. Assuming a uniform column density over the entire DLA system, we estimate its mass to be $M_{DLA}\geq5.3\times 10^6~M_\odot$. The extended illuminator and the low redshift of this DLA give us the unique opportunity to characterize its nature and the connection to its host galaxy. We measure a velocity offset of +131 km s$^{-1}$ from the systemic velocity of the host for the DLA. This velocity is $-84$ km s$^{-1}$ from the projected rotation velocity of the host galaxy as measured using a newly constructed rotation curve. Based on the size of the host galaxy, the HI column density, and the gas kinematics, we believe this DLA is tracing the warm neutral gas in the HI disk of the foreground galaxy. Our detection adds to a small set of low-redshift DLAs that have confirmed host galaxies, and is the first to be found using an extended background source.