The hypothesis that a stock market price index follows a random walk is tested for the regional stock market of the West African Economic and Monetary Union called the Bourse Regionale des Valeurs Mobilieres (BRVM) using the Lo and MacKinlay (1988), the Chow and Denning (1993), and the Wright’s (2000) rank-based variance ratio tests. The tests are applied to daily stock price index over the period January 2, 2002 to December 31, 2004, and all three tests reveals that the null hypothesis of random walk can not be rejected in the BRVM. This result is an indication that the BRVM is weak form efficiency and has various implications for investors and regulators. The first would engage their savings into productive investments opportunities and the second will limit their intervention as securities are fairly priced.