  Topological physics and strong electron-electron correlations in quantum
materials are typically studied independently. However, there have been rapid
recent developments in quantum materials in which topological phase transitions
emerge when the single-particle band structure is modified by strong
interactions. We here demonstrate that the room-temperature phase of
(TaSe$_4$)$_2$I is a Weyl semimetal with 24 pairs of Weyl nodes. Owing to its
quasi-1D structure, (TaSe$_4$)$_2$I hosts an established CDW instability just
below room temperature. Using X-ray diffraction, angle-resolved photoemission
spectroscopy, and first-principles calculations, we find that the CDW in
(TaSe$_4$)$_2$I couples the bulk Weyl points and opens a band gap. The
correlation-driven topological phase transition in (TaSe$_4$)$_2$I provides a
route towards observing condensed-matter realizations of axion electrodynamics
in the gapped regime, topological chiral response effects in the semimetallic
phase, and represents an avenue for exploring the interplay of correlations and
topology in a solid-state material.
