We perform a microscopic calculation to investigate how the chiral state (d) over cap (k) = (k(x) +/- ik(y))(z) over cap is stabilized in the triplet superconductor Sr2RuO4. Starting from the three band Hubbard model with spin-orbit interaction, we estimate the superconducting instability using the perturbation theory. The D-vector is microscopically determined by taking the spin-orbit interaction into account. It is shown that the chiral state is stabilized under the reasonable condition. The p-wave symmetry of order parameter and the properties of the gamma-band are essential for the chiral state. (C) 2003 Elsevier Science B.V. All rights reserved.