A ball and socket conveyor chain, the links of which are designed so as to be capable of flexing in a plurality of planes and also designed to have upper table portions for supporting articles to be conveyed and which include a ball portion and a socket portion integrally made a part of the table portion. The ball portion of one link is retained in the socket portion of an adjacent link by a cap having outer surfaces that are drivingly engagable by some drive means. The method of connecting the links is unique in that the successive links comprising the chain are not connected to each other, but rather to every other link in the chain.