Preheat oven to 425 degrees . Adjust racks to the middle of the oven.
Place room temperature butter, minced garlic and thyme and mix together in a small bowel. Mash with a fork. set aside
Rinse chicken thighs and pat dry with a paper towel.
Set chicken on cutting board. Lift the chicken skin from the top of the thigh and add 1 tablespoon of the herb butter mixture under the chicken skin. Evenly press the chicken skin so the butter appears to be evenly spread under the chicken skin. Set aside.
Heat two tablespoons of butter over medium heat in a large stainless steel skillet.
Add chopped onions and stir. Lower heat to medium/low heat, cover for approx 12 minutes ( or until tender) Onions should be tender.
Uncover and stir onions. Cook on medium heat for approximately 5 minutes ( or until golden brown)
Add salt and pepper to taste. Remove onions from skillet and place in a bowl. Set aside.
Heat olive oil in skillet on medium/high heat. With a spatula scrape up the onion particles.
Add salt and pepper to one side of the chicken thighs. Place in skillet. Sear chicken thigh ( approx 2-3 minutes)
Add salt and pepper to the uncooked side of the chicken thigh. Turn chicken thigh over and sear the other side ( approx 2- 3 minutes)
Add mushrooms to the skillet and place in oven for approx 12-15 minutes. Thermometer should read 165 F.
Have oven mitts on hand. Remove chicken thighs and let them rest for about 5 minutes. Remove the mushrooms and set aside.
This is what will make the sauce.
Over low/medium heat, deglaze the pan with 1/4 cup of red wine. Take the spatula and scrape the the skillet. Remove from heat.
Pass sauce through a fine strainer or sieve into a Pyrex( or other heat proof bowl) Add salt and pepper to taste
Place skillet over low heat, add the onions and mushrooms back into the sauce and heat it till warm.
Place chicken on the place and add sauce over it.