Generating laboratory flows resembling atmospheric turbulence is of prime importance to study the effect of wind fluctuations on objects such as buildings, vehicles, or wind turbines. A novel driving of an active grid following a stochastic process is used to generate velocity fluctuations with correlation lengths, and, thus, integral scales, much larger than the transverse dimension of the wind tunnel. The combined action of the active grid and a modulation of the fan speed allows one to generate a flow characterized by a four-decade inertial range and an integral scale Reynolds number of 2×10^{7}.