The secondary osteon - a fundamental building block in compact bone - is a multilayered cylindrical structure of mineralized collagen fibrils arranged around a blood vessel. Functionally, the osteon must be adapted to the in vivo mechanical stresses in bone at the level of its microstructure. However, questions remain about the precise mechanism by which this is achieved. By application of scanning x-ray diffraction with a micron-sized synchrotron beam, along with measurements of local mineral crystallographic axis direction, we reconstruct the three-dimensional orientation of the mineralized fibrils within a single osteon lamella ( approximately 5 mum). We find that the mineralized collagen fibrils spiral around the central axis with varying degrees of tilt, which would - structurally - impart high extensibility to the osteon. As a consequence, strains inside the osteon would have to be taken up by means of shear between the fibrils.