Let's leave before the sun rises.

Literal

Sun [subject-が] rise-not [during-うち-に] depart-[volitional-よう].

~ないうちに ('while X hasn't yet happened / before X happens') is a fixed temporal pattern — 'during the [state of not] X.' Subtly different from ~前に ('before X'): うちに emphasizes the time span during which the non-event holds, before which you should act.