Can I play Rengar trophy hunter on a reaction chain on a battlefield where I do not have units but my opponent does?

Yes. Rengar, Trophy Hunter can be played as a Reaction (during a Closed State) to a battlefield that has enemy units, even if you control no units there.

His card text explicitly expands the Ambush keyword: "I can [Ambush] to a battlefield where there are enemy units, even if you don't have units there." This overrides the normal Ambush requirement that you control units at the destination (Rule 822.1.b), and it also extends the conditional Reaction timing to cover that scenario — so you can play him during a Closed State (a "reaction chain") as long as an enemy unit is present at the target battlefield.

The key limit: the battlefield must be occupied by at least one enemy unit. An open battlefield (unoccupied and uncontrolled) won't work — Rengar's permission requires enemy units to be there (FAQ #11470).