In a 4-quart stockpot on medium heat, saute the onions and garlic with the olive oil, oregano, salt, and pepper until the onions are translucent, 10 to 15 minutes. Add the carrots, potatoes, 1/2 pound of split peas, and chicken stock. Bring to a boil, then simmer uncovered for 40 minutes. Skim off the foam while cooking. Add the remaining split peas and continue to simmer for another 40 minutes, or until all the peas are soft. Stir frequently to keep the solids from burning on the bottom. Taste for salt and pepper. Serve hot.