  Cosmology relies on the Cosmological Principle, i.e., the hypothesis that the
Universe is homogeneous and isotropic on large scales. This implies in
particular that the counts of galaxies should approach a homogeneous scaling
with volume at sufficiently large scales. Testing homogeneity is crucial to
obtain a correct interpretation of the physical assumptions underlying the
current cosmic acceleration and structure formation of the Universe. In this
Letter, we use the Baryon Oscillation Spectroscopic Survey to make the first
spectroscopic and model-independent measurements of the angular homogeneity
scale $\theta_{\rm h}$. Applying four statistical estimators, we show that the
angular distribution of galaxies in the range 0.46 < z < 0.62 is consistent
with homogeneity at large scales, and that $\theta_{\rm h}$ varies with
redshift, indicating a smoother Universe in the past. These results are in
agreement with the foundations of the standard cosmological paradigm.
