Heat a large pot to medium heat and add the oil.
Add the onion, peppers and celery and cook them until softened, about 5 minutes.

Add the garlic and ham and cook another minute, stirring, until fragrant.

Add the seasonings, blackeyed peas and chicken broth. Bring to a quick boil, then reduce the heat.

Simmer for 1 hour, or until the beans are nicely softened, but not mushy.
Serve over rice.