  The low-lying continuum spectrum of the $^6{\rm He}$ nucleus is investigated
for the first time within an ab initio framework that encompasses the $^4{\rm
He}$+$n$+$n$ three-cluster dynamics characterizing its lowest decay channel.
This is achieved through an extension of the no-core-shell model combined with
the resonating-group method, in which energy-independent non-local interactions
among three nuclear fragments can be calculated microscopically starting from
realistic nucleon-nucleon interactions and consistent ab initio many-body wave
functions of the clusters. The three-cluster Schr\"odinger equation is solved
with three-body scattering boundary conditions by means of the
hyperspherical-harmonic method on a Lagrange mesh. Using a soft
similarity-renormalization-group evolved chiral nucleon-nucleon potential, we
find the known $J^\pi = 2^+$ resonance as well as a result consistent with a
new low-lying second $2^+$ resonance recently observed at GANIL at $2.6$ MeV
above the $^6$He ground state. We also find resonances in the $2^-$, $1^+$ and
$0^-$ channels, while no low-lying resonances are present in the $0^+$ and
$1^-$ channels.
