  We utilize various {\em ab initio} approaches to search for a low-lying
resonance in the four-neutron ($4n$) system using the JISP16 realistic $NN$
interaction. Our most accurate prediction is obtained using a $J$-matrix
extension of the No-Core Shell Model and suggests a $4n$ resonant state at an
energy near $E_r = 0.8$ MeV with a width of approximately $\Gamma = 1.4$ MeV.
