BPMN choreography is a modeling language capable to describe scenarios where several independent participants have to collaborate in a climate of opposing interests and therefore are forced to trust each other. For this reason, in many contexts, a strong need for transparency, responsibility, and choreography compliance arise by the various participants. Blockchains and smart contracts, thanks to their characteristic of providing a decentralized and consensus-based validation mechanism, seem to be able to meet these needs in an untrusted scenario. Nevertheless, most of the related work focused either on transparency, accountability, or compliance, but none on all three of them. Furthermore, such works do not take into account the nondeterministc nature of choreographies. This work aims at using blockchains and smart contracts in this scenario providing a formally well-defined set of tools to match all three the aforementioned requirements. This work applies the proposed techniques to a case study from the construction industry, an economical relevant application domain where the demand for transparency, accountability, and compliance with procurement contracts (that can be modeled as choreographies) is very strong.