Compact chromatin is linked to a poor tumour prognosis and resistance to radiotherapy from photons. We investigated DNA damage induction and repair in the context of chromatin structure for densely ionising alpha radiation as well as its therapeutic potential. Chromatin opening by histone deacetylase inhibitor trichostatin A (TSA) pretreatment reduced clonogenic survival and increased gamma H2AX foci in MDA-MB-231 cells, indicative of increased damage induction by free radicals using gamma radiation. In contrast, TSA pretreatment tended to improve survival after alpha radiation while gamma H2AX foci were similar or lower; therefore, an increased DNA repair is suggested due to increased access of repair proteins. MDA-MB-231 cells exposed to fractionated gamma radiation (2 Gy x 6) expressed high levels of stem cell markers, elevated heterochromatin H3K9me3 marker, and a trend towards reduced clonogenic survival in response to alpha radiation. There was a higher level of H3K9me3 at baseline, and the ratio of DNA damage induced by alpha vs. gamma radiation was higher in the aggressive MDA-MB-231 cells compared to hormone receptor-positive MCF7 cells. We demonstrate that heterochromatin structure and stemness properties are induced by fractionated radiation exposure. Gamma radiation-exposed cells may be targeted using alpha radiation, and we provide a mechanistic basis for the involvement of chromatin in these effects.