Bose-Einstein condensates subject to short pulses (`kicks') from standing waves of light represent a nonlinear analogue of the well-known chaos paradigm, the quantum kicked rotor. We review briefly our current understanding of dynamicalor exponential instability in weakly kicked BECs. Previous studies of the onset of dynamical instability associated it with some form of classical chaos. We show it is due to parametric instability : resonant driving of certain collective modes. We map the zones of instability and calculate the Liapunov exponents.