Fully autonomous navigation using nano drones has numerous applications in the real world, ranging from search and rescue to source seeking. Nano drones are well-suited for source seeking because of their agility, low price, and ubiquitous character. Unfortunately, their constrained form factor limits flight time, sensor payload, and compute capability. These challenges are a crucial limitation for the use of source-seeking nano drones in GPS-denied and highly cluttered environments. Hereby, we introduce a fully autonomous deep reinforcement learning-based light-seeking nano drone. The 33-gram nano drone performs all computation on-board the ultra-low-power microcontroller (MCU). We present the method for efficiently training, converting, and utilizing deep reinforcement learning policies. Our training methodology and novel quantization scheme allow fitting the trained policy in 3 kB of memory. The quantization scheme uses representative input data and input scaling to arrive at a full 8-bit model. Finally, we evaluate the approach in simulation and flight tests using a Bitcraze CrazyFlie, achieving 80% success rate on average in a highly cluttered and randomized test environment. Even more, the drone finds the light source in 29% fewer steps compared to a baseline simulation (obstacle avoidance without source information). To our knowledge, this is the first deep reinforcement learning method that enables source seeking within a highly constrained nano drone demonstrating robust flight behavior. Our general methodology is suitable for any (source seeking) highly constrained platform using deep reinforcement learning.