Observations of occultations of bright γ-ray sources by the Sun may reveal predicted pair halos around blazars and/or new physics, such as, e.g., hypothetical light dark matter particles-axions. We use Fermi Gamma-Ray Space Telescope (Fermi) data to analyze four occultations of blazar 3C 279 by the Sun on October 8 each year from 2008 to 2011. A combined analysis of the observations of these occultations allows a point-like source at the position of 3C 279 to be detected with significance of ≈3σ, but does not reveal any significant excess over the flux expected from the quiescent Sun. The likelihood ratio test rules out complete transparency of the Sun to the blazar γ-ray emission at a 3σ confidence level.