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On January 1st 2019, the New Horizons spacecraft flew by the classical Kuiper belt object (486958) Arrokoth (provisionally designated 2014 MU69), possibly the most primitive object ever explored by a spacecraft. The I/F of Arrokoth is analyzed and fit with a photometric function that is a linear combination of the Lommel-Seeliger (lunar) and Lambert photometric functions. Arrokoth has a geometric albedo of p_V = 0.21_(-0.04)^(+0.05) at a wavelength of 550 nm and ~0.24 at 610 nm. Arrokoth's geometric albedo is greater than the median but consistent with a distribution of cold classical Kuiper belt objects whose geometric albedos were determined by fitting a thermal model to radiometric observations. Thus, Arrokoth's geometric albedo adds to the orbital and spectral evidence that it is a cold classical Kuiper belt object. Maps of the normal reflectance and hemispherical albedo of Arrokoth are presented. The normal reflectance of Arrokoth's surface varies with location, ranging from ~0.10-0.40 at 610 nm with an approximately Gaussian distribution. Both Arrokoth's extrema dark and extrema bright surfaces are correlated to topographic depressions. Arrokoth has a bilobate shape and the two lobes have similar normal reflectance distributions: both are approximately Gaussian, peak at ~0.25 at 610 nm, and range from ~0.10-0.40, which is consistent with co-formation and co-evolution of the two lobes. The hemispherical albedo of Arrokoth varies substantially with both incidence angle and location, the average hemispherical albedo at 610 nm is 0.063 +/- 0.015. The Bond albedo of Arrokoth at 610 nm is 0.062 +/- 0.015.