Can you chain reactions?

Yes — you can. Once a chain exists the turn is in a Closed State, and only Reaction-speed cards and abilities can be added to it, so any number of Reactions can stack on top of each other (Rule 309.1.a, 813).

They resolve last-in-first-out, and there's a fresh priority window after each item resolves — both players get a chance to add another Reaction before the next item resolves. So you can keep the chain going at every step, not just at the initial play.

One limit: a Reaction is still a Reaction. You can't slip an Action, a unit, or a non-Reaction activated ability onto an existing chain — wait for it to clear.