Heat oil in heavy large skillet over medium-high heat.
Add shallots and oregano and sauté until shallots are tender, about 5 minutes.
Season chicken with salt and pepper.
Add chicken, skin side down, to skillet and sauté until skin browns, about 5 minutes.
Using tongs, turn chicken over.
Add tomatoes and broth and bring to boil.
Cover skillet.
Reduce heat to medium-low.
Simmer until chicken is just cooked through, about 10 minutes.
Transfer chicken to plate.
Boil sauce over high heat until thickened, about 5 minutes.
Mix in cheese and simmer until heated through, about 5 minutes.