  We consider the Painleve asymptotics for a solution of integrable coupled
Hirota equationwith a 3*3 Lax pair whose initial data decay rapidly at
infinity. Using Riemann-Hilbert techniques and Deift-Zhou nonlinear steepest
descent arguments, in a transition zone defined by /x/t-1/(12a)/t^2/3<=C, where
C>0 is a constant, it turns out that the leading-order term to the solution can
be expressed in terms of the solution of a coupled Painleve II equation
associated with a 3*3 matrix Riemann-Hilbert problem.
