We prove the existence of a new branch of solutions of Mountain Pass type for the periodic 3-body problem with choreographical constraint. At first we describe the variational structure of the action functional associated to the choreographical three body problem in \mathbbR³\mathbb{R}^{3}. In the second part, using a bisection algorithm, we provide a numerical non-rigorous solution of Mountain Pass type for this problem in a rotating frame with angular velocity 1.5. The last step consists in the rigorous computer-assisted proof of the existence of a full branch of solutions for the problem starting from the Mountain Pass solution detected numerically.