In a large stockpot, bring 3 cups of water to a boil. Add the clams, cover, and cook for 5 minutes. Uncover the pot and quickly stir the clams with a wooden spoon. Cover and cook 5 to 10 minutes longer (this will depend on the type and size of the clams), or until most of the clams are open.
Transfer the clams to a large bowl or baking dish and strain the broth twice through a fine-mesh sieve into a bowl, being careful to strain out the sand. (You should have about 8 cups of clam broth. If not, add enough water to bring the volume up to 8 cups.) When the clams are cool enough to handle, remove them from their shells and chop into 1/2-inch pieces. Set the clams and broth aside.
Cook the bacon in a large stockpot over medium heat until golden and crispy, about 3 minutes. Pour off all the fat except 4 tablespoons. Add the onions, celery, bell peppers, and carrots and cook until softened, about 10 minutes. Add the garlic, bay leaves, oregano, thyme, and crushed red pepper and cook an additional 2 minutes. Increase the heat to high and add the potatoes, reserved clam broth, and Chicken Stock and bring to a boil, covered. Reduce to a simmer and cook until the potatoes are tender and the broth has thickened somewhat, about 20 minutes. Add the tomatoes and juice and tomato paste and continue to cook for 10 to 15 minutes. Remove the pot from the heat and add the reserved clams, the cilantro, and the black pepper and season to taste with salt.
Set the chowder aside for 1 hour, covered, to allow the flavors to marry. Place the pot over low heat and slowly reheat, being careful not to bring to a boil. Serve hot, garnished with more cilantro.
Makes 3 quarts, 10 servings