  This letter presents the first lattice QCD computation of the coupled channel
$\pi\Sigma-\bar{K}N$ scattering amplitudes at energies near $1405\,{\rm MeV}$.
These amplitudes contain the resonance $\Lambda(1405)$ with strangeness $S=-1$
and isospin, spin, and parity quantum numbers $I(J^P)=0(1/2^-)$. However,
whether there is a single resonance or two nearby resonance poles in this
region is controversial theoretically and experimentally. Using single-baryon
and meson-baryon operators to extract the finite-volume stationary-state
energies to obtain the scattering amplitudes at slightly unphysical quark
masses corresponding to $m_\pi\approx200$ MeV and $m_K\approx487$ MeV, this
study finds the amplitudes exhibit a virtual bound state below the $\pi\Sigma$
threshold in addition to the established resonance pole just below the
$\bar{K}N$ threshold. Several parametrizations of the two-channel $K$-matrix
are employed to fit the lattice QCD results, all of which support the two-pole
picture suggested by $SU(3)$ chiral symmetry and unitarity.
