One-month-ahead streamflow forecasting is important for water utilities to manage water resources such as irrigation water usage and hydropower generation. While deterministic streamflow forecasts have been utilized extensively in research and practice, ensemble streamflow forecasts and probabilistic information are gaining more attention. This study aims to examine a multivariate linear Bayesian regression approach to provide probabilistic streamflow forecasts by incorporating gridded precipitation forecasts from climate models and lagged monthly streamflow data. Principal component analysis is applied to reduce the size of the regression model. A Markov Chain Monte Carlo (MCMC) algorithm is used to sample from the posterior distribution of model parameters. The proposed approach is tested on gauge data acquired during 1961–2000 in North Carolina. Results reveal that the proposed method is a promising alternative forecasting technique and that it performs well for probabilistic streamflow forecasts.