Environmental concerns raise the need for more efficiency and sustainability in the freight transportation sector. For this purpose, the Physical Internet is introduced, which aims to connect logistics networks into one hyperconnected supernetwork. To transport freight over such an integrated network, the innovative concept of synchromodality is presented. Synchromodality is defined by the usage of multiple modalities when planning shipments, where real-time switching between transportation modes is possible. In this work, we introduce a synchromodal planning model that constructs optimal transportation routes in a multimodal network with stochastic transit times, formulated as a mixed-integer linear programming problem. To cope with the transit time stochasticity, transportation routes are adapted in accordance to real-time information about the transit time outcome. In a numerical study, we demonstrate the potential advantages that synchromodality entails in terms of costs, service quality and environmental impact.