Heat the oil in a large saucepan, or if your slow cooker has a browning function, then use this. Brown the chicken thighs for about 10 mins, until they have a nice golden colour, then remove and set aside. Tip in the bacon and celery, and brown these, too.
Tip everything apart from the lemon juice and 1 tbsp tarragon into your slow cooker. Simmer on High for 4-6 hrs, until the chicken is really tender and falling off the bone.
Check the sauce; if you like it a little thicker, strain liquid into a pan and boil until thickened.
Sprinkle in the lemon juice and remaining tarragon, season, then return chicken, bacon and veg if you need to.