Place the chicken breasts into a sandwich bag and lightly flatten them with a rolling pin. You want the whole breast to be a relatively even width.
Season each breast with salt and pepper, then heat some oil and the butter in a frying pan over a medium to high heat.
Cook the chicken for 3 to 5 minutes on each side. Once golden, remove the chicken and set aside.
Add the diced onion to the pan and cook until it softens, then chuck in the garlic and cook for a further minute.
Pour in the white wine and simmer for a minute so that it reduces by half.
Add the chicken stock, cream, and tarragon, then return the chicken to the pan. Let it simmer for a few minutes until the sauce starts to thicken.
Season to taste and serve. This is a super versatile dish that will pair well with rice, potatoes or even pasta.