  Using the concept of $d$-collapsibility from combinatorial topology, we
define chordal simplicial complexes and show that their Stanley-Reisner ideals
are componentwise linear. Our construction is inspired by and an extension of
"chordal clutters'' which was defined by Bigdeli, Yazdan Pour and Zaare-Nahandi
in 2017, and characterizes Betti tables of all ideals with linear resolution in
a polynomial ring.
  We show $d$-collapsible and $d$-representable complexes produce componentwise
linear ideals for appropriate $d$. Along the way, we prove that there are
generators that when added to the ideal, do not change Betti numbers in certain
degrees.
  We then show that large classes of componentwise linear ideals, such as
Gotzmann ideals and square-free stable ideals have chordal Stanley-Reisner
complexes, that Alexander duals of vertex decomposable complexes are chordal,
and conclude that the Betti table of every componentwise linear ideal is
identical to that of the Stanley-Reisner ideal of a chordal complex.
