Skin the breasts and slice the meat vertically, across the grain of the meat, into even-sized thin escalopes – about 4 pieces per breast. Season with salt and pepper.
Step 2 : Sear the chicken
Heat a large frying pan over a medium heat and add the oil. Add the chicken pieces one at a time, ensuring they are not on top of each other. Leave them alone in the pan to allow a nice crust to form. Turn over and cook for another 2-3 minutes as above.
Step 3 : Add the mushrooms
Add the butter and quartered chestnut mushrooms to the pan, moving them around in the butter for a good colour. Pour in the wine and deglaze, scraping all the flavour and caramelised pieces from the bottom of the pan. Reduce by half, then add the stock plus 2 tablespoons of the strained mushroom soaking liquid and reduce by half again.
Step 4 : Finish the sauce
Add the cream and chopped tarragon and bring to a simmer. Further reduce the sauce by a quarter until it has a good coating consistency on the back of a spoon. Check the seasoning.
Step 5 : To serve
Serve on warmed plates with boiled new potatoes and buttered green beans on the side.