Heat olive oil and butter in a large saute pan until the butter melts then add chicken and cook until browned.
Add the mushrooms, shallots and tarragon and cook until the mushrooms become tender and the chicken is cooked through.
Add the wine and mustard to the pan and stir until blended, then reduce to low, cover and simmer about 10-15 minutes.
Remove the lid, make a space/well in the center of the pan by moving all the ingredients to the sides and then add the chevre to the center of the pan and mix it with a little cream, stir some, mix in more cream, stir more, etc, until chevre is blended in and cream is incorporated.
Mix chicken and mushrooms into cream sauce, check again for seasonings and serve.
I served this along side wild rice, but you can do as you like.