The olivine macrocrysts found in oceanites, picrites and magnesian basalts erupted at hotspot volcanoes are generally interpreted either as phenocrysts crystallized from the magma or as xenocrysts extracted from a deforming cumulate. To constrain the origin of these crystals we studied their texture and composition at Piton de la Fournaise volcano, La Réunion. We show that macrocrysts are organized and subdivided into parallel units; this suggests a crystallization by dendritic growth and ripening rather than by a complex combination of paired nucleation, crystal aggregation or synneusis. Dendritic growth is also evidenced by the occurrence of hollow faces, P-rich zones, melt and Cr-spinel inclusions formed from the accumulation of slow diffusing impurities (P, Cr, Al) in the liquid at the contact with rapid-growing olivine. We suggest that early dendritic crystallization may even cause branch misorientations and lattice mismatches, yielding subgrain boundaries, dislocation lamellae and to a certain extent undulose extinction, which have all been formerly interpreted in terms of plastic intracrystalline deformation. We interpret olivine macrocrysts as phenocrysts crystallized under a strong degree of undercooling (-ΔT > 60°C), and derived from a harrisitic mush formed on the cold walls of the magma reservoir. Given the growth shapes indicated by P zoning patterns and external faces, the olivine macrocrysts (which consist of groups of several subcrystals) have grown in suspension within the liquid and were neither aggregated into a dense cumulate nor corroded, shocked or deformed before or during their transport to the surface. The major consequence of our study is that most olivine macrocrysts are not xenocrysts, and very few of them, if any, have experienced intracrystalline deformation. The importance of deforming (creeping) cumulate bodies, thought to accommodate the spreading of basaltic volcanoes in La Réunion and Hawaii, may hence have been overestimated.