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We present the discovery of DELVE 6, an ultra-faint stellar system identified in the second data release of the DECam Local Volume Exploration (DELVE) survey. Based on a maximum-likelihood fit to its structure and stellar population, we find that DELVE 6 is an old ( τ > 9.8 Gyr at 95% confidence) and metal-poor ([Fe/H] < −1.17 dex at 95% confidence) stellar system with an absolute magnitude of ${M}_{V}=-{1.5}_{-0.6}^{+0.4}$ mag and an azimuthally averaged half-light radius of ${r}_{1/2}={10}_{-3}^{+4}$ pc. These properties are consistent with the population of ultra-faint star clusters uncovered by recent surveys. Interestingly, DELVE 6 is located at an angular separation of ∼10° from the center of the Small Magellanic Cloud (SMC), corresponding to a 3D physical separation of ∼20 kpc given the system’s observed distance ( D _⊙ = 80 kpc). This also places the system ∼35 kpc from the center of the Large Magellanic Cloud (LMC), lying within recent constraints on the size of the LMC’s dark matter halo. We tentatively measure the proper motion of DELVE 6 using data from Gaia, which we find supports a potential association between the system and the LMC/SMC. Although future kinematic measurements will be necessary to determine its origins, we highlight that DELVE 6 may represent only the second or third ancient ( τ > 9 Gyr) star cluster associated with the SMC, or one of fewer than two dozen ancient clusters associated with the LMC. Nonetheless, we cannot currently rule out the possibility that the system is a distant Milky Way halo star cluster.