Brush each half peach with olive oil from both sides.
Preheat grill pan over medium-high heat. When the pan is hot, place on top several peaches, cut side down. Cook until grill marks appear, 3-5 minutes. Invert the peaches and cook for another few minutes, until grill marks appear on the skin and the fruits start to soften.
In a salad bowl combine baby spinach, rucola, avocados and onion. Add salt, oil and vinegar and mix well.
Divide the salad between four serving plates. Place on each one a piece of cooked and sliced chicken breast and two halves grilled peaches. Serve immediately.
In case you don’t have a grill pan, you can toast the peaches on a normal frying pan or skillet.