  We provide experimental and theoretical evidence for the realization of the
Peierls-type structurally distorted state in the quasi-one-dimensional
superconductor Sc$_3$CoC$_4$ by a phonon-softening mechanism. The transition
from the high- to the final low-temperature phase below 80K proceeds via an
extended intermediate temperature regime between 80K and 150K characterized by
phonon-driven atom displacements. In support of the low-dimensional character
of the title compound we find a highly anisotropic correlation-length of these
dynamic distortions.
