A turbomachine combustion chamber includes an inner annular wall, an outer annular wall surrounding the inner wall so as to co-operate therewith to define an annular space forming a combustion area, a plurality of fuel injector systems including pilot injectors alternating circumferentially with full-throttle injectors, and at least one air admission opening out into the upstream end of the combustion area in a substantially longitudinal direction. The outer wall has a plurality of pilot cavities extending between the two longitudinal ends of the outer wall and extending radially towards thereof, the pilot cavities being fed with air from outside the combustion chamber in a common substantially circumferential direction. Each pilot injector opens out radially into a pilot cavity, and each full-throttle injector opens out radially between two adjacent pilot cavities.