Direct numerical simulations of the transition process from steady laminar to chaotic flow are considered in this study with the relatively new incompressible lattice Boltzmann equation. Numerically, a multiple relaxation time fully incompressible lattice Boltzmann equation is implemented in a 2D driven cavity. Spatial discretization is 2nd-order accurate, and the Kolmogorov length scale estimation based on Reynolds number ($Re$) dictates grid resolution. Initial simulations show the method to be accurate for steady laminar flows, while higher $Re$ simulations reveal periodic flow behavior consistent with an initial Hopf bifurcation at $Re$ 7,988. Non-repeating flow behavior is observed in the phase space trajectories above $Re$ 13,063, and is evidence of the transition to a chaotic flow regime. Finally, flows at Reynolds numbers above the chaotic transition point are simulated and found with statistical properties in good agreement with literature.