1. Rinse chicken and pat dry. In a 10- to 12-inch nonstick frying pan over medium heat, combine chicken, onion, tomato, oil, garlic, and cumin. Stir often until chicken is slightly pink in center of thickest part (cut to test), 6 to 10 minutes.
2. Let stand until chicken is cool enough to touch, then tear meat into shreds. Return to pan. Add bell pepper, canned chilies, and cheese; mix.
3. Wearing rubber gloves, cut poblanos in half lengthwise. With a knife, cut seed lump from beneath the stem inside each chili, leaving stem end in place (to form a cup). Pull out and discard veins.
4. Mound chicken mixture equally in chili halves. Set chilies in an oiled 9- by 13-inch casserole, filling it. Cover tightly with foil.
5. Bake in a 375° oven until the poblanos are tender when pierced, about 35 minutes.
6. Serve chilies with a spatula. Add crème fraîche and salt to taste.