In this paper we present a process which enables privacy-preserving speech recognition transactions between two parties. We assume one party with private speech data and one party with private speech recognition models. Our goal is to enable these parties to perform a speech recognition task using their data, but without exposing their private information to each other. We will demonstrate how using secure multiparty computation principles we can construct a system where this transaction is possible, and how this system is computationally and securely correct. The protocols described herein can be used to construct a rudimentary speech recognition system and can easily be extended for arbitrary audio and speech processing.