Pound chicken breast to 1/4 to 1/2 inch thickness.
Wash jalapeno and pat dry; seed and remove ribs, if desired.
If using canned green chilies, rinse, seed and pat dry.
Chop chile.
Shred enough cheese to measure 1/4 cup.
In small bowl, combine cheese with chile, chopped cilantro and sour cream.
Set aside.
Heat broiler.
Line broiler tray with aluminum foil and set aside.
Sprinkle both sides of chicken breasts with salt and pepper to taste.
Combine butter and oil in large heavy-gauge skillet over medium-high heat.
Saute chicken breasts, 2 at a time, about 5 minutes per side, or until brown.
Transfer to broiler tray.
Top each chicken breast with a generous spoonful of sour-cream mixture.
Broil 4 to 5 inches from heating element about 5 minutes, or until topping bubbles.
Transfer to platter and serve immediately.
Ready in 30 min.