We present the first proper motion measurement for an ultra-faint dwarf spheroidal galaxy, Segue 1, using data from the Sloan Digital Sky Survey (SDSS) and the Large Binocular Camera (LBC) as the first and second epochs separated by a baseline of ∼10 years. We obtain a motion of μ α cos(δ) = ‑0.37 ± 0.57 mas yr‑1 and μ δ = ‑3.39 ± 0.58 mas yr‑1. Combining this with the known line-of-sight velocity, this corresponds to a Galactocentric V rad = 84 ± 9 and {V}\tan ={164}-55+66 km s‑1. Applying Milky Way halo masses of between 0.8 and 1.6 × 1012 M ⊙ results in an apocenter at {33.9}-7.4+21.7 kpc and pericenter at {15.4}-9.0+10.1 kpc from the Galactic center, indicating that Segue 1 is rather tightly bound to the Milky Way. Since neither the orbital pole of Segue 1 nor its distance to the Milky Way is similar to the more massive classical dwarfs, it is very unlikely that Segue 1 was once a satellite of a massive known galaxy. Using cosmological zoom-in simulations of Milky Way-mass galaxies, we identify subhalos on similar orbits as Segue 1, which imply the following orbital properties: a median first infall {8.1}-4.3+3.6 Gyr ago, a median of four pericentric passages since then, and a pericenter of {22.8}-4.8+4.7 kpc. This is slightly larger than the pericenter derived directly from Segue 1 and Milky Way parameters, because galaxies with a small pericenter are more likely to be destroyed. Of the surviving subhalo analogs, only 27% were previously a satellite of a more massive dwarf galaxy (that is now destroyed), thus Segue 1 is more likely to have been accreted on its own.