Place the cutup chicken breasts in a medium bowl. Season with 2 1/2 teaspoons of the spice mix.
In a deep non-stick pan, heat the olive oil over high heat.Note: The oil should be hot but not smoking.
Cook the chicken in 2 batches. Cook about 2 minutes on each side until nice and brown. Transfer to a plate/bowl - set aside.Note: Adjust heat if necessary.
Turn the heat to low. The oil will be very hot so lowering it before adding the onions is important to preven onions from browning.
Add the sliced onions and diced celery. Sprinkle in a pinch of the seasoning mix. Stir and saute 2 to 3 minutes.Note: Adjust the heat back up to medium if needed.You want the onions to become translucent - do not brown the onions.
Add in the crushed garlic and fresh thyme. Saute 30 to 60 seconds.
Add in the tomatoes, remaining spice mix and blackeye peas. Mix together. Bring to a boil. Cover. Reduce heat to low and simmer 8 to 10 minutes until tomatoes break down.
Add in the chicken breasts and any juices released. Cover and simmer 25 minutes over medium low heat.Note: I cook the chicken for this amount of time to allow the flavors to be absorbed into the meat.
Add in the olives, if using. Cover and cook for 5 minutes. Turn off the stove.
Plate and serve. Garnish with chopped parsley if preferred. I love to serve this recipe on a bed of rice. Enjoy.