In a large skillet over medium-low heat, melt butter. Brown chicken in hot butter, turning to brown both sides, about 8 to 10 minutes total. Remove from skillet.
Add shallot; sauté for about 5 minute, or until shallot is tender.
Stir in heavy cream, Dijon mustard, tarragon, salt, and pepper.
Add chicken back to skillet; heat to a simmer.
Cover and simmer over low heat until chicken is cooked, about 15 minutes.
Remove chicken from skillet.
Whisk sour cream into the sauce in skillet until smooth.
Serve the chicken with sauce spooned over chicken breasts and Dan-D-Pak country wild rice on side.
