Preheat the oven to 150°C.
Place a casserole dish over a medium heat and add the olive oil. When the oil is hot, add the chicken pieces and brown lightly.
Add the garlic and shallots, season with salt and pepper, and leave to cook for a further minute.
Pour the wine over the chicken and leave to simmer for 10 minutes. Pour in the chicken stock.
Add the tarragon to the casserole, stir and cover.
Cook in the oven for 11⁄2 hours. Cut into a thick portion of chicken and ensure that it is cooked through, with no pink showing.
Homemade by Clodagh McKenna, published by Kyle Cathie: With a strong focus on using local produce and eating together, Clodagh McKenna's new cookbook, Homemade brings together recipes and ideas gathered from years of travelling and taking notes. Order the book online.
For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home and view the full Food safety at home video.