In concentrated solution and in the presence of high concentrations of mono
valent cations, nucleosome core particles order into a discotic columnar me
sophase. This phase is limited to finite-sized hexagonal germs that further
divide into six coiled branches, following an iterative process. We show h
ow the structure of the germs comes from the competition between hexagonal
packing and chirality with a combination of dendritic facetting and double-
twist configurations. Geometrical considerations lead us to suspect that th
e chirality of the eukaryotic chromosomes may originate from the same compe
tition.