We report on a NICER observation of the Galactic X-ray binary and stellar-mass black hole candidate, MAXI J1535-571. The source was likely observed in an "intermediate" or "very high" state, with important contributions from both an accretion disk and hard X-ray corona. The 2.3-10 keV spectrum shows clear hallmarks of relativistic disk reflection. Fits with a suitable model strongly indicate a near-maximal spin parameter of a = cJ/GM^2 = 0.994(2) and a disk that extends close to the innermost

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... able circular orbit, r/r_ISCO = 1.08(8) (1-sigma statistical errors). In addition to the relativistic spectrum from the innermost disk, a relatively narrow Fe K emission line is also required. The resolution of NICER reveals that the narrow line may be asymmetric, indicating a specific range of emission radii. Fits with a relativistic line model suggest an inner radius of r = 144 (+140,-60) GM/c^2 for the putative second reflection geometry; full reflection models suggest that radii a few times larger are possible. The origin of the narrow line is uncertain but a warp likely provides the most physically plausible explanation. We discuss our results in terms of the potential for NICER to reveal new features of the inner and intermediate accretion disk around black holes.