We use two-body potentials derived from a constituent quark cluster model to analyze the bound-state problem of the ΣNN system. The observables of the two-body subsystems, NN and ΣN, are well reproduced. We do not find ΣNN bound states, but there are two attractive channels with a resonance close above the three-body threshold. These channels are the (I,J)=(1,1/2) and (0,1/2), their quantum numbers, widths and energy ordering consistent with the recently reported strange tribaryons from the He4(Kstopped-,N) reactions in the KEK PS E471 experiment. © 2006 The American Physical Society.