Measurements of the UV-continuum slopes β provide valuable information on the physical properties of galaxies forming in the early universe, probing the dust reddening, age, metal content, and even the escape fraction. While constraints on these slopes generally become more challenging at higher redshifts as the UV-continuum shifts out of the Hubble Space Telescope bands (particularly at z > 7), such a characterization actually becomes abruptly easier for galaxies in the redshift window z = 9.5-10.5 due to the Spitzer/Infrared Array Camera 3.6 μm-band probing the rest-UV continuum and the long wavelength baseline between this Spitzer band and the Hubble Hf160w band. Higher S/N constraints on β are possible at z ˜ 10 than at z = 8. Here, we take advantage of this opportunity and five recently discovered bright z = 9.5-10.5 galaxies to present the first measurements of the mean β for a multi-object sample of galaxy candidates at z ˜ 10. We find the measured βobs's of these candidates are -2.1 ± 0.3 ± 0.2 (random and systematic), only slightly bluer than the measured β's (βobs ≈ -1.7) at 3.5 <z <7.5 for galaxies of similar luminosities. Small increases in the stellar ages, metallicities, and dust content of the galaxy population from z ˜ 10 to z ˜ 7 could easily explain the apparent evolution in β.