We present the discovery and subsequent spectroscopy with Gemini-North of the optical afterglow of the Swift gamma-ray burst (GRB) 140515A. The spectrum exhibits a well-detected continuum at wavelengths longer than 8915 Angs with a steep decrement to zero flux blueward of 8910 Angs due to Ly-alpha absorption at redshift z~6.33. Some transmission through the Lyman-alpha forest is present at 5.2<z<5.733, but none is detected at higher redshift, consistent with previous measurements from quasars and GRB 130606A. We model the red damping wing of Lyman-alpha in three ways that provide equally good fits to the data: (a) a single host galaxy absorber at z=6.327 with log(N_HI)=18.62+/-0.08; (b) pure intergalactic medium (IGM) absorption from z=6.0 to z=6.328 with a constant neutral hydrogen fraction of x_HI=0.056+0.011-0.027; and (c) a hybrid model with a host absorber located within an ionized bubble of radius 10 comoving Mpc in an IGM with x_HI=0.12+/-0.05 (x_HI<0.21 at the 2-sigma level). Regardless of the model, the sharpness of the dropoff in transmission is inconsistent with a substantial neutral fraction in the IGM at this redshift. No narrow absorption lines from the host galaxy are detected, indicating a host metallicity of [Z/H]<~ -0.8. Even if we assume that all of the hydrogen absorption is due to the host galaxy, the column is unusually low for a GRB sightline, similar to two out of the other three highest-redshift bursts with measured log(N_HI). This is possible evidence that the escape fraction of ionizing photons from normal star-forming galaxies increases at z>~6.
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