Electron hole transport along DNA chains is studied theoretically. Couplings between the DNA bases adenine, cytosine, guanine, and thymine, placed as in DNA in a single strand or diagonally in a double strand, are calculated using ab initio methods. Coupling as well as reorganization energies, which are also calculated, show a great variation between bases. To decide whether a periodic DNA strand has localized or delocalized electrons, a novel theoretical model that uses reorganization energy and coupling as input, is used. The model suggests that electron holes on infinite one-dimensional chains of periodic DNA localize if the ratio of reorganization energy to coupling is larger than about four. The hole is weakly trapped on an infinite guanine strand (G)(chi) whereas it is elocalized in thymine (T)(chi) and cytosine (C)(chi) strands. Some mixed DNA strands also show a delocalized behavior, but most are localized to a single G in agreement with EPR measurements. Rates of stepwise hole transfer between G sites in mixed chains are calculated and show agreement with experimental data. In electron-transfer steps between localized sites, the tunneling rate decreases exponentially with distance with a quite large beta factor in agreement with earlier theoretical work.