If you do want to use boneless skinless breast in cacciatore type dish, brown the chicken separately, which takes just a few minutes, check it frequently and as soon as the inside is no longer pink, get it off the heat.
Then prepare the sauce separately and serve the sauce over the chicken, or cut the chicken in bite sizes and mix them into the sauce when the sauce is ready. It is not the same, but at least it is much better than rubbery chicken!!
If you want the flavours of the chicken and the sauce better integrated, try a good quality thigh meat to cook in the sauce, as Andy suggested.