Soak skewers in cold water for 30 minutes. Cut chicken thighs into 1” cubes. Thread 3 cubes onto wooden skewer. Repeat with remain skewers. Brush chicken with olive oil and sprinkle salt and pepper. Grill skewers over medium heat until cooked through and golden, about 7 to 8 minutes per side.
For sauce; place large skillet over medium heat. Add butter and oil. Add mushrooms and garlic. Cook until mushrooms give up their liquid. In bowl combine ½ cup chicken broth and flour. Whisk until smooth and add half of the mixture to mushrooms - reserve the other half for additional thickening, if needed. Add Marsala and remaining ½ cup of chicken broth to mushrooms. Cook until thickened - stirring constantly for approx 5 to 7 minutes (add remaining thickening mixture if needed). Season to taste with salt and pepper. Serve sauce over skewers and serve.