Pat the chicken strips dry with paper towels. Place some flour for dusting in a bowl and season with salt and pepper. Add the chicken strips and toss to coat in the seasoned flour.
Heat the butter and oil in a medium frying pan over a medium heat. Add the chicken strips in batches and fry until brown on all sides. Return all the chicken to the pan.
Add a generous amount of the tarragon, reserving a little for garnish. Add the stock and orange juice to cover the chicken. Simmer gently for about 10 minutes until the chicken is cooked through.
Remove the chicken from the pan with a slotted spoon and put in a shallow serving dish with the orange segments. Keep warm.
Continue to simmer the stock until reduced by half, then add the cream and reduce again until you have a thick sauce. Taste, season and add some of the reserved juices from the orange segments if it needs to be sharpened.
Spoon the sauce over the chicken and serve garnished with the reserved tarragon.