Season chicken breasts with salt and pepper. In a large skillet, heat oil over medium heat. Cook chicken breasts over medium heat for about 5-7 minutes on each side or until done. Remove from pan and keep warm.
Add chicken broth to the pan, scraping the bits from bottom of the pan. Whisk in tarragon, Dijon mustard and milk. Let simmer for 1-2 minutes, whisking constantly, until thickened. Serve over chicken breasts.