Two reference priors for the product of means ofnnormal distributions with common known variance are developed. One of them induces an improper posterior distribution and therefore is not of much interest. The other is a generalized form of then= 2 case derived by Berger and Bernardo. The latter is compared with the uniform prior (the Jeffreys prior) in posterior inference and the optimal frequentist coverage criterion. The reference prior is shown to be better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile, by numerical computation. The computation was performed by Gibbs sampling forn= 3 andn= 10. Furthermore, it is shown that the reference prior is among the asymptotic optimal frequentist coverage probability priors under a transformation of the parameter space such that the parameter of interest and the nuisance parameters are orthogonal. In an example, the Bayesian credible interval for the product of normal means using the reference prior is compared to the confidence interval using the method of Yfantis and Flatman.