Heat olive oil in a skillet over medium-high heat. Pound chicken breast to 1/2-inch thickness. Dredge breasts in flour to lightly coat on each side. Salt and pepper on each side. Sauté chicken breasts until golden. Remove chicken to a baking dish and place in the oven while the sauce is made.
Remove excess oil from the skillet. Add shallots and sauté until tender. Add the vermouth and simmer until reduced by half.
Add the raspberry jam, lime juice and salt. Stir and heat until combined.
Check chicken to make sure it is cooked through and the juices run clear. Add the chicken back to the skillet. Cover with sauce. Serve garnished with chopped chives.