Optical chaos generated by perturbing semiconductor lasers has been viewed, over recent decades, as an excellent entropy source for fast physical random bit generation (RBG) owing to its high bandwidth and large random fluctuations. However, most optical-chaos-based random bit generators perform their quantization process in the electrical domain using electrical analog-to-digital converters, so their real-time rates in a single channel are severely limited at the level of Gb/s due to the electronic bottleneck. Here, we propose and experimentally demonstrate an all-optical method for RBG where chaotic pulses are quantized into a physical random bit stream in the all-optical domain by means of a length of highly nonlinear fiber. In our proof-of-concept experiment, a 10-Gb/s random bit stream is successfully generated on-line using our method. Note that the single-channel real-time rate is limited only by the chaos bandwidth. Considering that the Kerr nonlinearity of silica fiber with an ultrafast response of few femtoseconds is exploited for composing the key part of quantizing laser chaos, this scheme thus may operate potentially at much higher real-time rates than 100 Gb/s provided that a chaotic entropy source of sufficient bandwidth is available.