I modeled it in Interactive Physics- rectangles for the links of the chain-
non-elastic ropes connecting them- a 12 link chain beats a single
rectangle neatly.
I took a box of jumbo paper clips. I made a chain about 2 meters long,
suspended so the last clip will just hit a horizontal board. I dropped the
end of the chain and a single paper clip at the same time. The end of the
chain beats the paper clip.
Initially all links fall together, but as the lowest link is swung around to
stop its outboard end pulls down on the link above it, pulling down on the
link above it, etc. in the whipping action described by others. A loosely
linked chain cannot apply compression, but can apply tension- that's what
chains are for!