  We compute the shift of the transition temperature for a homogenous weakly
interacting Bose gas in leading order in the scattering length a for given
particle density n. Using variational perturbation theory through six loops in
a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c =
1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.
