This specimen is somewhat unique in what is normally found, it contains very visible mesocorallites quadrilaterals. It is described as a new species in Erwin Stumm's Silurian and Devonian Corals of the Falls of the Ohio on page 79 as Halysites louisvillensis (Stumm, 1964). Stumm writes about it, "The species is externally similar to Catenipora microparus (Whitfield) but differs in the presence of the very small mesocorallites."
Most of the specimens of chain corals I have seen, one cannot see the little square shapes in between the chain shapes. It is possible they are there but after hundreds of millions of years they blended together obscuring the four sided shape.
This fossil is found in the Louisville Limestone of Jefferson County Kentucky USA. It dates to the Middle Silurian Period.