If I react to a charm by playing an Ambush Rengar which immediately resolves, will my opponent then have a window after that to react to their own charm on the chain?

Yes, your opponent will have an opportunity to react to their own Charm after your Rengar, Trophy Hunter has finished entering play.

Here is the breakdown of how this interaction proceeds:

1. Chain State: When you play Rengar, Trophy Hunter as a [Reaction] to Charm, the chain is in a "Closed State" (it contains the Charm spell).
2. Playing the Permanent: You follow the process of playing a card. Once you finish finalizing Rengar, he is no longer "Pending" (Rule 359.1).
3. Entering Play: Per Rule 359.2, as a Permanent, Rengar leaves the chain and becomes a game object. He enters the board at the chosen location (exhausted) (Rule 359.2.c).
4. Priority/Reaction Window: According to RiftJudge FAQ #2028, as soon as a permanent (a unit or gear) resolves and enters play, the player who controls the next item on the chain (in this case, your opponent, who controls the Charm spell) gains priority.
   • This gives your opponent an opportunity to add a new [Reaction] to the chain, or simply allow the chain to continue resolving.
   • If they pass, you would then receive priority, and so on, until both players pass in sequence.
5. Resolution: Only after both players have passed priority consecutively without adding anything new to the chain does the topmost item (the Charm spell) resolve.

Summary: Your opponent does not lose their chance to react to their own spell. Once your unit has entered play, the priority system resumes, and all players retain the standard opportunity to add reactions to the chain before the next spell on the chain resolves.