Cook bacon in a deep 12-inch heavy skillet over moderately low heat, stirring, until crisp, about 8 minutes. Transfer with a slotted spoon to paper towels to drain and reserve bacon fat in skillet.
While bacon is cooking, Rinse chicken, pat dry with paper towels, and season both sides with salt and pepper. Heat oil in a large, high-sided sauté pan over medium-high. Working in batches, brown chicken on both sides, turning once, 10 to 12 minutes. Transfer chicken to a platter; tent loosely with parchment paper, then foil, to keep warm.
Add onions, tomatoes, and thyme to the pan. Cook, stirring occasionally, until golden brown, about 4 minutes. Pour in Marsala; cook until reduced by half, about 5 minutes. Return chicken to pan and pour in stock; bring to a simmer, and cover. cook until chicken is cooked through and tender, about 35 minutes. Transfer chicken to a platter, and cover to keep warm.
Skim off excess fat from liquid in pan; simmer liquid over medium-high until slightly thickened, about 5 minutes. To serve, divide polenta among shallow bowls and arrange chicken on top; spoon pan sauce over each.