Observations of occultations of bright. gamma-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 theSun 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 3C279 to be detected with significance of approximate to 3 sigma, 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. gamma-ray emission at a 3s confidence level.