A child-resistant container closure includes a base cap having a top, a skirt, and a plurality of asymmetric teeth recessed in the skirt below the top, and a cover cap having a top, a skirt, and a plurality of asymmetric downwardly extending teeth adjacent to the skirt, the teeth being adapted for asymmetric engagement with the base cap teeth, the skirt having a plurality of interspersed vertical legs each spaced apart from adjacent legs by vertical openings, the legs being joined at a bottom end of the skirt by a support ring, the base cap teeth each having a sloped sliding face to ensure that one of the cover cap teeth will drop into a notch between adjacent base cap teeth when the cover cap is rotated in one direction.