  With a view to understanding the ``rheochaos'' observed in recent experiments
in a variety of orientable fluids, we study numerically the equations of motion
of the spatiotemporal evolution of the traceless symmetric order parameter of a
sheared nematogenic fluid. In particular we establish, by decisive numerical
tests, that the irregular oscillatory behavior seen in a region of parameter
space where the nematic is not stably flow-aligning is in fact spatiotemporal
chaos. We outline the dynamical phase diagram of the model and study the route
to the chaotic state. We find that spatiotemporal chaos in this system sets in
via a regime of {\em spatiotemporal intermittency}, with a power-law
distribution of the widths of laminar regions, as in H. Chat\'{e} and P.
Manneville, Phys. Rev. Lett. {\bf 58}, 112 (1987). Further, the evolution of
the histogram of band sizes shows a growing length-scale as one moves from the
chaotic towards the flow aligned phase. Finally we suggest possible experiments
which can observe the intriguing behaviors discussed here.
