Abstract
We present an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a 4x4 matrix spectral problem. An integrable coupled mKdV hierarchy with three potentials is first generated. Based on the corresponding oscillatory Riemann-Hilbert problem, the leading asympototics of the three-component mKdV system is then evaluated by using the nonlinear steepest descent method.