Can Challenge be played during the chain of Star Crossed?

No, you cannot play Challenge in response to Star-Crossed.

Reasoning:

• Challenge is an [Action] card (as confirmed by its card data).
• According to Rule 309.1.a and Rule 331.1.a, cards of all categories (by default) cannot be played during a Closed State (when a chain exists). [Action] cards can only be played in an Open State (when no chain exists).
• Star-Crossed is a [Reaction] card. When played, it creates a chain, putting the game into a Closed State.
• Because the game is in a Closed State while Star-Crossed is on the chain, only cards or abilities with the [Reaction] keyword can be played. Since Challenge is an [Action], it is not a legal play at that time.

This interaction is also supported by RiftJudge FAQ #4454, which clarifies that Challenge (as an Action) cannot be played in response to other cards once a chain has been started.