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 heavy pot over medium heat until crisp and the fat is rendered. Pour off all the bacon fat except 2 tablespoons. Add the 4 tablespoons butter, leeks, onions, and celery and cook until softened, about 5 minutes. Add the garlic, thyme, and bay leaves and cook until the vegetables are thoroughly wilted, about 3 minutes, being careful not to brown. Add the potatoes and reserved clam broth and bring to a boil. Lower the heat, cover, and simmer until the broth thickens slightly and the potatoes are very tender, about 30 minutes. (If you like a thicker broth, mash some of the potatoes against the side of the pot with a wooden spoon.). Remove from the heat, Discard the thyme stems and bay leaves, stir in the clams and cream, and season with the pepper and the salt to taste.
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 let boil. Serve hot; garnish each bowl with a pat of butter and some parsley and chives.