Trim the extra skin and fat off the chicken thighs and season with salt and pepper
Combine basil, tarragon, and thyme in a small bowl mix well
Dice the shallots
In a large skillet, heat olive oil and 2 tbsp butter over medium high heat
When the oil is hot, place the chicken in the pan skin side down
Sprinkle the top of the chicken with about half the mixed herbs and cook for 3-4 minutes until the skin is browned
Turn the heat down to medium and flip the chicken
Sprinkle the remaining mixed herbs on the chicken and cover the pan.
Cook for 16-20 minutes until the chicken is done
Remove the chicken from the pan and cover with aluminum foil to let it rest
Put the shallots in the pan and cook for about 1 minute. Add the garlic and cook for a minute more.
Add the chicken broth to the pan and deglaze any remaining chicken bits from the pan
Lower the heat and simmer until the liquid is reduced by about half, stirring often.
Remove the pan from the heat and add the remaining 2 tbsp of butter. Stir well to melt the butter and thicken the sauce. You can also whisk the sauce to better emulsify it.
Serve the sauce over the chicken. If you serve with rice or mashed potatoes, drizzle some sauce on them as well.