In a large stockpot bring 2 cups of water to a boil. Add clams, cover and cook for 5 minutes. Uncover, quickly stir clams with a wooden spoon. Cover and cook 5 to 10 minutes longer (this will depend on the type and size of clams you are using), or until most of the clams are opened.

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 6 cups of clam broth. If not, add enough water to bring the volume up to 6 cups.) When the clams are cool enough to handle, remove them from their shells and chop into 1/2-inch pieces. Set clams and broth aside.

In a large heavy pot cook the bacon until crisp and the fat is rendered. Pour off all bacon fat except 2 tablespoons. Add the butter, 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 for 20 to 30 minutes, or until the broth thickens slightly and the potatoes are very tender. (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, stir in clams and heavy cream and season with pepper and salt, if necessary.

Set 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 the boil. Serve hot, garnished with 1 or 2 pats of butter, parsley and chives.