Deep Reinforcement Learning (DRL) is applied to control a nonlinear, chaotic system governed by the one-dimensional Kuramoto-Sivashinsky (KS) equation. DRL uses reinforcement learning principles for the determination of optimal control solutions and deep Neural Networks for approximating the value function and the control policy. Recent applications have shown that DRL may achieve superhuman performance in complex cognitive tasks. In this work, we show that using restricted, localized actuations, partial knowledge of the state based on limited sensor measurements, and model-free DRL controllers, it is possible to stabilize the dynamics of the KS system around its unstable fixed solutions, here considered as target states. The robustness of the controllers is tested by considering several trajectories in the phase-space emanating from different initial conditions; we show that the DRL is always capable of driving and stabilizing the dynamics around the target states. The complexity of the KS system, the possibility of defining the DRL control policies by solely relying on the local measurements of the system, and their efficiency in controlling its nonlinear dynamics pave the way for the application of RL methods in control of complex fluid systems such as turbulent boundary layers, turbulent mixers or multiphase flows.