Drain pineapple, reserving syrup.
In a Dutch oven, cook pork, half at a time, in hot olive oil until brown. Return all the meat to the pot. Add the first chopped onion and 1 clove garlic. Cook over medium heat until onion is tender, stirring occasionally.
Add the reserved pineapple syrup, undrained tomatoes, tomato paste, green chili peppers, green sweet pepper, 1 onion, chili powder, jalapeno pepper, cumin, the 2 cloves garlic, and the salt.
Bring to boiling. Reduce heat. Cover and simmer the chili for 1-1/2 hours, stirring occasionally. Add the pineapple chunks. Cover and simmer for 30 minutes more.
Let diners add their own toppers. Makes 8 to 10 servings.
To increase the spiciness of the chili, add 2 more tablespoons of the jalapeno pepper.