Dice the peppers.
Heat the oil in a frying pan and put in the peppers, cover and let cook 5-7 minutes. Season lightly with salt. Keep a tablespoon of peppers aside and put the rest in a blender with olive oil to make a nice smooth cream. Do not wash the pan.
Use the same skillet to cook the diced chicken. Brown it well for about 5 minutes. The pieces should be cooked but not overcooked so they do not become dry. Season lightly with salt.
Mix all the ingredients together (if you have too much bell pepper cream, do not drown the chicken but keep it aside), then add the remaining peppers, just a little salt if needed, ground pepper and fresh herbs.
Serve immediately or at room temperature.