PRE-HEAT OVEN TO 450º
RINSE OUT THE CHICKEN CAVITY. DRY WITH PAPER TOWELS. SEASON CAVITY WITH SALT AND PEPPER. STUFF IT WITH SEVERAL SPRIGS OF THYME AND 1/2 LEMON. TRUSS THE CHICKEN OR TIE THE LEGS TOGETHER. DRY OUTSIDE OF THE CHICKEN AND SEASON WITH SALT AND PEPPER.
CUT THE GARLIC HEADS IN HALF HORIZONTALLY. SEPARATE THE CLOVES, BUT DON'T BOTHER TO PEEL THEM.
HEAT A CAST IRON PAN FOR 5 MINUTES ON TOP OF THE STOVE. SPLASH A LITTLE OLIVE OIL IN THE HOT PAN AND PLACE THE CHICKEN IN THE PAN. SEAR FOR 5 MINUTES. REMOVE THE CHICKEN TO A PLATE.
MAKE A BED FOR THE CHICKEN WITH THE GARLIC CLOVES. PLACE THE CHICKEN ON TOP AND PUT IN THE OVEN. ROAST FOR ABOUT 50 MINUTES OR UNTIL THE JUICES RUN CLEAR.
PLACE THE CHICKEN UPSIDE DOWN ON A WARM PLATTER. CUT AWAY THE TRUSSING STRINGS AND TAKE OUT THE LEMON.
POUR 3/4 CUP OF WHITE WINE INTO THE PAN AND BOIL DOWN WITH THE GARLIC TO ABOUT 1/2 CUP. SQUEEZE A FEW TBSPS OF LEMON JUICE FROM THE COOKED LEMON INTO THE PAN.
PLACE A STRAINER OVER A SMALL SAUCEPAN. SCRAPE THE GARLIC AND DRIPPINGS INTO THE STRAINER. USING A RUBBER SCRAPER MUSH THE GARLIC THROUGH THE STRAINER LEAVING THE PEEL BEHIND.
ADD THE CRÉME FRAÎCHE TO THE SAUCEPAN, BRING TO A BOIL AND REDUCE TO ABOUT 3/4 CUP.
TURN OFF THE HEAT. STIR IN A FEW DOLLOPS OF BUTTER.
CHOP TARRAGON AND STIR INTO THE SAUCE.
ARRANGE THE CHICKEN BREAST SIDE UP ON YOUR SERVING PLATTER AND SPOON THE SAUCE OVER IT. GARNISH WITH A FEW TARRAGON LEAVES.
SERVE WITH STEAMED RICE, RICE PILAF OR ORZO PASTA.
SERVES 4