Charge transport through the DNA double helix is of fundamental interest in chemistry and biochemistry, but also has potential technological applications such as for DNA-based nanoelectronics. For the latter, it is of considerable interest to explore ways to influence or enhance charge transfer. In this Article we demonstrate a new mechanism for DNA charge transport, namely 'deep-hole transfer', which involves long-range migration of a hole through low-lying electronic states of the nucleobases. Here, we demonstrate, in a combined experimental and theoretical study, that it is possible to achieve such transfer behaviour by changing the energetics of charge injection. This mechanism leads to an enhancement in transfer rates by up to two orders of magnitude and much weaker distance dependence. This transfer is faster than relaxation to the lowest-energy state, setting this mechanism apart from those previously described. This opens up a new direction to optimize charge transfer in DNA with unprecedented charge-transfer rates.