Sauté shallot and garlic in heated butter. Take out the garlic. Add flour and sweat. Deglaze with the broth and cream and simmer for 2-3 minutes, stirring constantly.
Rinse the tarragon, shake dry and stir finely chopped into the sauce. Season to taste with salt, pepper, sugar and lemon juice.
Salt and pepper the chicken breast. Fry in hot fat for 12-15 minutes. Slice the chicken breast and serve with the sauce.