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We present the discovery of a candidate ultra-faint Milky Way satellite,Eridanus IV (DELVE J0505$-$0931), detected in photometric data from the DECamLocal Volume Exploration survey (DELVE). Eridanus IV is a faint ($M_V = -4.7\pm 0.2$), extended ($r_{1/2} = 75^{+16}_{-13}$ pc), and elliptical ($\epsilon= 0.54 \pm 0.1$) system at a heliocentric distance of $76.7^{+4.0}_{-6.1}$ kpc,with a stellar population that is well-described by an old, metal-poorisochrone (age of $\tau \sim 13.0$ Gyr and metallicity of ${\rm [Fe/H] \lesssim-2.1}$ dex). These properties are consistent with the known population ofultra-faint Milky Way satellite galaxies. Eridanus IV is also prominentlydetected using proper motion measurements from Gaia Early Data Release 3, witha systemic proper motion of $(\mu_{\alpha} \cos \delta, \mu_{\delta}) = (+0.25\pm 0.06, -0.10 \pm 0.05)$ mas yr$^{-1}$ measured from its horizontal branchand red giant branch member stars. We find that the spatial distribution oflikely member stars hints at the possibility that the system is undergoingtidal disruption.

Eridanus IV: an Ultra-Faint Dwarf Galaxy Candidate Discovered in the DECam Local Volume Exploration Survey