We present a Monte Carlo study of the two-component $ϕ^4$ model on the simple cubic lattice in three dimensions. By suitable tuning of the coupling constant $λ$ we eliminate leading order corrections to scaling. High statistics simulations using finite size scaling techniques yield $ν=0.6723(3)[8]$ and $η=0.0381(2)[2]$, where the statistical and systematical errors are given in the first and second bracket, respectively. These results are more precise than any previous theoretical estimate of the critical exponents for the 3D XY universality class. Comment: 13 pages