Heat olive oil in a large skillet over medium high heat. Pat the chicken thighs dry and sprinkle them with salt and pepper. Place the chicken in the skillet skin side down and allow to brown, without moving or turning, for about 4 minutes. When the chicken is well-browned and will lift easily from the skillet, flip and repeat on the other side. Remove chicken from pan and set aside.
Prepare the artichokes: follow the directions in the above post for trimming the fresh baby artichokes, or if using frozen or canned, gently pat them dry with a paper towel. Place the artichokes in the pan, cut side down, and allow them to take on a bit of color without moving or flipping. When they begin to brown, Add the garlic and shallot, and stir. Allow the garlic to brown in spots and begin to soften, stirring every two minutes for about 6 minutes.
Add the vermouth to the pan and scrape up any browned bits clinging to the pan. Add the chicken stock and stir. Bring to a simmer, and tuck the browned chicken thighs into the sauce. Sprinkle with a little salt and pepper.
Put a lid on the pan and allow it to simmer for about 15 minutes to finish cooking the chicken and marry the flavors together. Remove the lid and add the green olives and about half of the oregano and stir. Allow it to cook another 5 minutes. Check to ensure that the chicken is cooked through, giving it a few more minutes if necessary. When done, the chicken will be fork-tender.
This chicken dish is wonderful served on a bed of pasta, rice, farro, or polenta. Garnish with the remaining oregano and serve.