Place chicken breasts on a cutting board, and pound thin with a mallet.
Heat oil in a large skillet over medium-high heat. Stir in onions and garlic. Place chicken in skillet and brown on both sides. Add 1 cup chicken broth, reduce heat to medium low; cover, and simmer for 10 minutes. Remove skillet from heat.
Meanwhile, melt butter in a medium saucepan over low heat. Gradually stir in flour, stirring until smooth. Increase heat to medium, and cook briefly until thickened. Stir in milk, lime juice, and tomato paste; cook until it begins to thicken, about 25 minutes. Stir in 1/2 cup chicken broth to thin sauce, and warm through. Remove from heat, and stir in rosemary and shrimp.
To serve, remove chicken, onions, and garlic to plates with a slotted spoon, and top with sauce.