Slightly brown the chicken breasts on each side in the butter+olive oil. Remove from pan
Soften the shallots in the same pan. Then add the cream, the wine and the tarragon
Simmer gently, adjust the seasoning and when hot return the chicken to the pan. Cover and simmer for a further 5 mins or so just until the chicken is cooked through
Serve immediately with a generous helping of the sauce poured over