We have studied the transport properties of a device consisting of two quantum dots, defined electrostatically in a (Al,Ga)As heterostructure. In the series conductance of the two dots, we observe irregularly spaced conductance peaks of fluctuating amplitude. This behaviour results from transport in the stochastic Coulomb blockade regime. In a second experiment, we measure the charging energy of one dot through the effect of its potential (which varies in a saw-tooth fashion with gate voltage) on the conductance of the other dot. We find that the charging energy scales quadratically with the reflection probability of the tunnel barriers, in agreement with a recent theory.