  In many of the experimental systems that may host Majorana zero modes, a
so-called chiral symmetry exists that protects overlapping zero modes from
splitting up. This symmetry is operative in a superconducting nanowire that is
narrower than the spin-orbit scattering length, and at the Dirac point of a
superconductor/topological insulator heterostructure. Here we show that chiral
symmetry strongly modifies the dynamical and spectral properties of a chaotic
scatterer, even if it binds only a single zero mode. These properties are
quantified by the Wigner-Smith time-delay matrix $Q=-i\hbar S^\dagger dS/dE$,
the Hermitian energy derivative of the scattering matrix, related to the
density of states by $\rho=(2\pi\hbar)^{-1}\,{\rm Tr}\,Q$. We compute the
probability distribution of $Q$ and $\rho$, dependent on the number $\nu$ of
Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral
symmetry is essential for a significant $\nu$-dependence.
