We present a true random number generator which, contrary to other implementations, is not based on the explicit observation of complex micro-cosmic processes but on standard signal processing primitives, freeing the designer from the need for dedicated hardware. The system can be implemented from now ubiquitous analog-to-digital converters building blocks, and is therefore well-suited to embedding. On current technologies, the design permits data rates in the order of a few tens of megabits per second. Furthermore, the absence of predictable, repeatable behaviors increases the system security for cryptographic applications. The design relies on a simple inner model based on chaotic dynamics which, in ideal conditions, can be formally proven to generate perfectly uncorrelated binary sequences. Here, we detail the design and we validate the quality of its output against a couple of test suites standardized by the U.S. National Institute of Standards and Technology, both in the ideal case and assuming implementation errors.