Chain production system entrusted to the formation of the link via a spiralling machine and a rotating pin. “Spiral” machines are chain making machines whose link formation is entrusted to a pin/spiral system, whereby the wire winds around a rotating pin, positioned inside a spiral that ensures a constant wire winding pitch, to take on a helicoidal or spiral shape, with each revolution of the pin, a pair of grippers receives a portion of the spiral, which is cut by a pair of blades; the grippers then place the portion of the spiral between a pair of facons, or clamps, which close it in the shape of the link, the newly formed link can remain coplanar, and be used for a Forzatina chain, or else the grippers can rotate the link still held by the facon to give it the shape of a Gourmette link. In both cases, the grippers still holding the newly produced link deposit it onto the next spiral, giving rise to the chain.