Pound the chicken breasts to an even 1/4" thickness.
In a deep skillet or pot over medium-high heat add the butter and olive oil, add the chicken and sear 3-4 minutes per side.
Pour the beer into the pan, cook over medium heat 10 minutes covered then uncover the last 5 minutes or until the chicken is completely cooked through, occasionally spooning liquid over the top of the chicken. Transfer the chicken to a plate or cutting board to cool while you make the sauce.
In the same skillet, add the olive oil, onion and garlic and cook over medium heat until the onions are soft, stirring occasionally so the garlic doesn't burn.
Add the ketchup, Worcestershire, sriracha, beer, apple cider vinegar, brown sugar and tarragon. Simmer over low heat 5-7 minutes or until the sauce thickens.
While the sauce is simmering, use two forks or your fingers and shred the chicken.
After the sauce has thickened, taste it and if you’d like a spicier sauce, add more sriracha. Blend the shredded chicken into the sauce, combining thoroughly.