A compact source, G0.02467–0.0727, was detected in Atacama Large Millimeter/submillimeter Array 3 mm observations in continuum and very broad line emission. The continuum emission has a spectral index α ≈ 3.3, suggesting that the emission is from dust. The line emission is detected in several transitions of CS, SO, and SO2 and exhibits a line width FWHM ≈ 160 km s−1. The line profile appears Gaussian. The emission is weakly spatially resolved, coming from an area on the sky ≲1″ in diameter (≲104 au at the distance of the Galactic center, GC). The centroid velocity is v LSR ≈ 40–50 km s−1, which is consistent with a location in the GC. With multiple SO lines detected, and assuming local thermodynamic equilibrium (LTE) conditions, the gas temperature is T LTE = 13 K, which is colder than seen in typical GC clouds, though we cannot rule out low-density, subthermally excited, warmer gas. Despite the high velocity dispersion, no emission is observed from SiO, suggesting that there are no strong (≳10 km s−1) shocks in the molecular gas. There are no detections at other wavelengths, including X-ray, infrared, and radio. We consider several explanations for the millimeter ultra-broad-line object (MUBLO), including protostellar outflow, explosive outflow, a collapsing cloud, an evolved star, a stellar merger, a high-velocity compact cloud, an intermediate-mass black hole, and a background galaxy. Most of these conceptual models are either inconsistent with the data or do not fully explain them. The MUBLO is, at present, an observationally unique object.