Melt the butter in a nonstick skillet over medium-high heat.
Add the shallots and saute, stirring occasionally, for 2 to 3 minutes, or until they start to soften.
Add the mushrooms, 1/4 teaspoon of the salt and 1/8 teaspoon of the pepper, and saute for 5 to 6 minutes until the mushrooms soften.
Add the sherry and cook 1 to 2 minutes, or until most of the liquid has evaporated.
Remove from the heat and keep warm.
Sprinkle the remaining 1/4 teaspoon of salt, 1/8 teaspoon of pepper and the rosemary over the chicken.
Coat a ridged grill pan or cast-iron skillet with the olive oil and heat over medium high.
Add the chicken and cook 5 to 6 minutes on each side, or until the chicken is cooked through.
(A thermometer, inserted horizontally into the center of the breast, should register 160 degrees).
Place a chicken breast on each plate and serve topped with the sauteed mushrooms.