New ages for flowstone, sediments and fossil bones from the Dinaledi Chamber are presented. We combined optically stimulated luminescence dating of sediments with U-Th and palaeomagnetic analyses of flowstones to establish that all sediments containing Homo naledi fossils can be allocated to a single stratigraphic entity (sub-unit 3b), interpreted to be deposited between 236 ka and 414 ka. This result has been confirmed independently by dating three H. naledi teeth with combined U-series and electron spin resonance (US-ESR) dating. Two dating scenarios for the fossils were tested by varying the assumed levels of 222Rn loss in the encasing sediments: a maximum age scenario provides an average age for the two least altered fossil teeth of 253 +82/-70 ka, whilst a minimum age scenario yields an average age of 200 +70/-61 ka. We consider the maximum age scenario to more closely reflect conditions in the cave, and therefore, the true age of the fossils. By combining the US-ESR maximum age estimate obtained from the teeth, with the U-Th age for the oldest flowstone overlying Homo naledi fossils, we have constrained the depositional age of Homo naledi to a period between 236 ka and 335 ka. These age results demonstrate that a morphologically primitive hominin, Homo naledi, survived into the later parts of the Pleistocene in Africa, and indicate a much younger age for the Homo naledi fossils than have previously been hypothesized based on their morphology.