Can I play an action card on the chain after an action card?

No, you cannot play an action card on the chain after an action card.

According to RiftJudge FAQ #2855 and RiftJudge FAQ #8949:

• Action cards can only be played to start a chain when the game state is "Open" (meaning no chain currently exists).
• Once an action card is played, the game state becomes "Closed." While a chain is active, only reaction cards may be added to it.
• You must wait for the current chain to resolve completely and the game state to return to "Open" before you can play another action card to start a new chain.