  We investigate low-lying bound states of the neutron-rich nucleus ${}^{15}$B
by assuming it is a three-body system made of an inert core ${}^{13}$B and two
valence neutrons. The three-body wave functions are obtained using the Faddeev
formalism. Special attention is paid to the excited state at $3.48(6)$ MeV
observed in the
${}^{13}\text{C}({}^{14}\text{C},{}^{12}\text{N}){}^{15}\text{B}$ reaction,
whose properties are less clear theoretically. In our three-body model, besides
the ground state $3/2_1^-$, a second $3/2_2^-$ state is discovered at around
$3.61$ MeV, which might be identified with the excited state observed at
$3.48(6)$ MeV. We study this $3/2_2^-$ state in detail, which turns out to be a
two-neutron halo state with a large matter radius $r_\text{m}\approx 4.770$ fm.
