The stochastic behavior of electrons during the interaction of an intense short laser pulse with under-dense plasma is investigated by employing a fully kinetic 1D-3V particle-in-cell (PIC) simulation. The development of chaos in the involved nonlinear regime and in the presence of plasma space charge is examined. Though the electron Lagrangian is extremely complicated in this case, our analyses suggest some potential ways for chaos development. In this regard, our simulation results show that chaotic motion can develop in three different ways. When the space charge field is weak, the scattered fields can provide the necessary condition for chaos to occur. When a strong space charge field is presented, the creation of chaos is initiated by wave breaking. The third procedure for creating chaos originates from the inhomogeneity of the density on the vacuum–plasma surface. In this case, a new electrostatic mode without any phase relation with the space charge electrostatic mode is generated.