The problem of local community detection refers to the identification of a community starting from a query node and using limited information about the network structure. Existing methods for solving this problem however are not designed to deal with multilayer network models, which are becoming pervasive in many fields of science. In this work, we present the first method for local community detection in multilayer networks. Our method exploits both internal and external connectivity of the nodes in the community being constructed for a given seed, while accounting for different layer-specific topological information. Evaluation of the proposed method has been conducted on real-world multilayer networks.