We predict that in arrays of quantum dots (0D superlattice) and arrays of one-dimensional quantum wires (1D superlattice) chaotic transport should be observed in the presence of an ac field and for a wide range of physical parameters, like the external dc bias, contact charge, doping levels, and disorder in the array. Time-dependent current oscillations set in the array due to the formation of electric domain walls when sequential resonant tunneling is the main transport mechanism between adjacent units. Such oscillations can then be forced into spatiotemporal chaos. A similar phenomenon has been predicted and demonstrated for solid-state superlattices. However, contrary to the latter case, the domain walls move across a larger number of units in the superlattice the lower the dimensionality, due to the different spatial distribution of the electric-field across the array in the three cases.