Heat oven to 250 degrees F (warm oven).
In a saucepan, combine chicken broth and carrots. Add bay leaves. Bring to a boil and cook until carrots are just tender, about 18-20 minutes. When carrots are tender, remove to a bowl. Reserve broth.
While carrots cook, season chicken thighs with salt and pepper. In a skillet that will hold chicken in a single layer, heat oil over medium high heat. Add chicken and sauté until brown, about 4-5 minutes per side. Remove chicken to an oven-safe dish and place in warm oven.
To the skillet, add wine, scraping up any brown bits on bottom of pan. Add reserved broth, bring to a boil, and reduce until liquid measures about 3/4 cup, about 12 minutes.
Add sour cream to pan, bring to a boil and reduce slightly. Sauce should measure about one cup. Add carrots and chopped tarragon and stir. Return chicken to pan, turning to coat in sauce. Remove to serving platter and garnish with tarragon sprigs.