The concept of fractional cointegration, whereby deviations from an equilibrium relationship are allowed to follow a fractionally integrated process, has attracted some attention in the literature of late. The long memory aspect of the fractional process is seen as an appropriate characterization of slow reversion to an equilibrium relationship. This paper presents a Bayesian method for conducting inference within the context of a fractional cointegration model. The analysis is based on an approximate likelihood function, which is motivated by the need both to solve a fundamental identification problem and to produce a posterior density with a relatively simple algebraic form. Inferences are based on the associated marginal posterior densities, estimated by a hybrid of the Gibbs and Metropolis Markov Chain Monte Carlo methods.