The growth of copper precipitate colonies in high‐purity dislocation‐free silicon single crystals has been examined by transmission electron microscopy. The colonies, being coplanar arrangements of copper‐silicide particles on either {110} or {100) planes, nucleate and grow during rapid cooling from higher temperatures. The kinetics of the colony growth process has been analyzed in terms of a model based on repeated nucleation on a climbing dislocation. The possibility of having the growing copper‐silicide particles dragged by the dislocations has been discussed, and a mechanism based on a particle dragging/dislocation climb effect has been suggested in order to explain the development of dendritic dislocation dipole branches.