In this talk, we introduce a rigorous computational method for periodic orbits of dissipative PDEs. The idea is to consider a space-time Fourier expansion of a periodic solution and to solve for its Fourier coefficients in a space of algebraically decaying sequences. The rigorous computation is based on the radii polynomials approach, which provide an efficient means of constructing a ball centered at a numerical approximation which contains a genuine periodic solution. We apply this method to show the existence of several periodic solutions in the Kuramoto-Sivashinsky equation. This is joint work with Marcio Gameiro (Sao Carlos, Brazil).