The virtualized network functions placement and chaining problem is formulated as a decision tree to reduce significantly the complexity of service function chaining (SFC) in clouds. Each node in the tree corresponds to a virtual resource embedding and each tree branch to the mapping of a client request in some physical candidate. This transforms the placement problem to a decision tree search. We devise a new algorithm based on the Monte Carlo Tree Search (MCTS) to incrementally build and search within the decision tree. Thanks to the proposed SFC-MTCS strategy, an optimized solution is computed in a reasonable time. Extensive simulations assess the performance and show that SFC-MCTS outperforms state of the art strategies in terms of: i) acceptance rate, ii) providers revenue and iii) execution time