Warm the olive oil in the skillet over medium heat. Add the quartered shallots, 2 stems of thyme, and the minced garlic. Cook until the shallots are translucent.
Place the chicken breast pieces in the pan and continue cooking over medium heat, turning after about 5 minutes. The chicken pieces should be browned on one side.
When the shallots are getting golden brown and a little caramelized around the edges and the chicken is browned on both sides, add the chopped sundried tomatoes and stir them in.
Sprinkle the salt and pepper over the chicken and add the white wine and the remaining thyme stems. Cook until the wine reduces and thickens a bit, about 3 to 5 minutes. Serve immediately.