Combine all marinade ingredients in a medium sized mixing bowl. Add chicken thighs and turn to coat. Set aside.
Preheat oven to 350 degrees F.
Add drizzle of olive oil to dutch oven and heat over MED-HIGH heat. Brown andouille sausage on both sides, then transfer sausage to a plate.
Add chicken thighs, skin side down, and sear for 2-3 minutes per side, to develop a nice crispy skin.
Transfer chicken to plate with the sausage, and use a paper towel to wipe out any black bits from the pan. Brown bits and pan drippings are good to leave in though.
Lower heat to MED-LOW and add in chopped onion, jalapeno and celery. Saute for about 2-3 minutes, until softened.
Add cayenne, red pepper flakes and salt and pepper and stir.
Add rice and chicken stock, give it a stir, and let simmer for 1 minute.
Nestle chicken thighs and sausage on top of the rice (pour in the juices that are left on the plate as well). Return to a simmer, then cover.
Bake at 350 degrees for 35 minutes (covered).
Remove cover and bake another 10-15 minutes, until liquid is absorbed into the rice.
Garnish with sliced green onions and minced parsley!