In a large pot add the olive oil and heat to meduim. Add the carrots, celery, kielbasa and saute until the onions are soft and the kielbasa is starting to brown. Add the blackeyed peas, tomatoes, chicken broth and seasoings.
Reduce heat to medium low until simmering then lower the heat to low. Place the lid of the pot loosely on top to allow some of the liquid to evaporate. Simmer for 45 minutes to an hour. Serve with crusty rolls or cornbread.