Provided is an engagement chain unit that has reliable and strong engagement and avoids buckling, breaking, and bending of a chain stiffening section. In the engagement chain unit (100), the engagement operation of an external tooth ring plate (112BZ) and an external tooth ring plate (112AY) that are just about to complete the engagement operation is completed in a manner that causes a first inter-pin distance (d1) and a second inter-pin distance (d2) to be approximately equivalent, and causes a third inter-pin distance (d3) to approach the second inter-pin distance (d2).