The evolution of an experimental braided river produced in our laboratory has been monitored and analyzed. It has been shown that in addition to the spatial scaling revealed by Sapozhnikov and Foufoula-Georgiou [1996a], braided rivers also exhibit dynamic scaling. This implies that a smaller part of a braided river evolves identically (in the statistical sense) to a larger one provided the time is renormalized by a factor depending only on the ratio of the spatial scales of those parts. The small value of the estimated dynamic exponent z is interpreted as an indication that the evolution of small channels in a braided river system is to a large extent forced by the evolution of bigger channels. The presence of dynamic scaling is further interpreted as indicating that braided rivers may be in a critical state and behave as self-organized critical systems.