  Charge-density-wave (CDW) order has long been interpreted as arising from a
Fermi-surface instability in the parent metallic phase. While phonon-electron
coupling has been suggested to influence the formation of CDW order in
quasi-two-dimensional (quasi-2D) systems, the presumed dominant importance of
Fermi-surface nesting remains largely unquestioned in quasi-1D systems. Here we
show that phonon-electron coupling is also important for the CDW formation in a
model quasi-1D system ZrTe$_3$. Our joint experimental and computational study
reveals that particular lattice vibrational patterns possess exceedingly strong
coupling to the conduction electrons, and are directly linked to the lattice
distortions associated with the CDW order. The dependence of the coupling
matrix elements on electron momentum further dictates the opening of (partial)
electronic gaps in the CDW phase. Since lattice distortions and electronic gaps
are the defining signatures of CDW order, our result demonstrates that the
conventional wisdom based on Fermi-surface geometry needs to be substantially
supplemented by phonon-electron coupling even in the simplest quasi-1D case. As
prerequisites for the CDW formation, the highly anisotropic electronic
structure and strong phonon-electron coupling in ZrTe$_3$ give rise to a
distinct Raman scattering effect, namely, measured phonon linewidths depend on
the direction of momentum transfer in the scattering process.
