Comets are thought to preserve almost pristine dust particles, thus providing a unique sample of the properties of the early solar nebula. The microscopic properties of this dust played a key part in particle aggregation during the formation of the Solar System. Cometary dust was previously considered to comprise irregular, fluffy agglomerates on the basis of interpretations of remote observations in the visible and infrared and the study of chondritic porous interplanetary dust particles that were thought, but not proved, to originate in comets. Although the dust returned by an earlier mission has provided detailed mineralogy of particles from comet 81P/Wild, the fine-grained aggregate component was strongly modified during collection. Here we report in situ measurements of dust particles at comet 67P/Churyumov-Gerasimenko. The particles are aggregates of smaller, elongated grains, with structures at distinct sizes indicating hierarchical aggregation. Topographic images of selected dust particles with sizes of one micrometre to a few tens of micrometres show a variety of morphologies, including compact single grains and large porous aggregate particles, similar to chondritic porous interplanetary dust particles. The measured grain elongations are similar to the value inferred for interstellar dust and support the idea that such grains could represent a fraction of the building blocks of comets. In the subsequent growth phase, hierarchical agglomeration could be a dominant process and would produce aggregates that stick more easily at higher masses and velocities than homogeneous dust particles. The presence of hierarchical dust aggregates in the near-surface of the nucleus of comet 67P also provides a mechanism for lowering the tensile strength of the dust layer and aiding dust release.