In a skillet over medium-high heat, brown chicken breasts on both sides in oil.
Don't worry about cooking through; just brown the outsides nicely; season with salt and pepper to taste.
Remove from skillet and place in slow cooker.
Reduce skillet heat to medium-low; add butter and melt. Add onions and carrots and saute until onions are lightly browned.
Add to slow cooker.
Pour chicken broth into skillet and scrape up the browned bits from the bottom of the pan; pour broth over chicken in slow cooker.
Add tarragon, thyme, bay leaf and potatoes. C
Cover and cook on low heat setting for about 6 hours, or until chicken is done.