Season each side of chicken breasts with salt and pepper. Heat olive oil in a heavy saute pan over medium-high heat; sear both sides of breasts until golden brown. Remove breasts from pan onto seperate plate and set aside. Deglaze the same pan with vermouth; add onion and garlic. Reduce heat to low; gently simmer to allow flavor of onion and garlic to impart into sauce. Add cream and allow to simmer slightly. Return chicken to pan; cover and finish cooking over low heat for 6-7 minutes, or until chicken reaches 160°F when a meat thermometer is inserted into the thickest part (or chicken is no longer pink and juices run clear when cut with a knife). Remove chicken breasts from the sauce; strain sauce. Add half the chopped tarragon to the sauce; set aside.
Combine creme fraiche, Dijon mustard, salt and pepper in a small bowl; fold in remaining chopped tarragon. Spoon the hot tarragon cream sauce over the chicken breasts and top with a small dollop of the tarragon Dijon creme fraiche.
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