This paper addresses Virtual Network Functions (VNFs) placement and chaining in the presence of physical link failures. A decision tree approach to the NP-Hard VNF placement and chaining problem is used to minimize the penalties induced by service interruptions due to link outages. Formulating the problem as decision tree reduces the complexity significantly and leads to a new reliable algorithm, named R-SFC-MCTS, that builds incrementally the decision tree to efficiently search for good placement and chaining solutions. Execution time is improved thanks to the Monte-Carlo Tree Search strategy. The proposed link failure recovery algorithm selects and assigns reliable paths to prevent and avoid the negative effects of link failures and reactively re-maps impacted virtual links in safer physical paths once an outage occurs in the infrastructure. The performance of R-SFC-MCTS is compared via extensive simulations with a baseline and a reactive solution in terms of: i) acceptance rate, ii) induced penalties iii) provider revenue loss and iv) the final provider's profit