Heat oil in a large deep skillet over mediumlow heat. Season chicken with salt and pepper. Cook in skillet, turning to brown all sides, 18 to 20 minutes.Transfer to a plate.
Add onions, peppers, potatoes, rosemary (if using), and 1/2 cup water to skillet; season with salt and pepper. Toss to combine, scraping any browned bits off bottom of skillet. Cover skillet, and simmer over medium heat, stirring occasionally, until potatoes begin to soften, 8 to 10 minutes (they will cook further in step 3).
Return chicken to skillet; add tomatoes. Cover skillet, and cook until chicken is opaque throughout and potatoes are tender, 8 to 10 minutes. Transfer chicken to serving plates. Stir parsley into vegetables in skillet; serve with chicken.