Bring clams and 4 cups water to a boil in a large pot over high heat. Cook until clams just open, 8-10 minutes (discard any that do not open). Using a large slotted spoon, transfer clams to a large rimmed baking sheet; set broth aside. Let clams cool slightly, then pull meat from shells; discard shells.

Chop clams into bite-size pieces. Strain broth through a fine-mesh sieve set over a large bowl. Add water if needed to measure 6 cups. DO AHEAD: Clams and broth can be made 1 day ahead. Cover separately and chill.

Melt butter in a large heavy pot over medium heat. Add bacon and cook, stirring occasionally, until fat is rendered and bacon begins to brown, about 8 minutes. Add celery, onion, and garlic and cook, stirring often, until onion is translucent, about 10 minutes. Add reserved broth (or 6 cups bottled clam juice), potatoes, thyme, and bay leaf. Bring chowder base to a simmer; cook until potatoes are tender, 20-25 minutes. Stir cornstarch and 2 tablespoons water in a small bowl to form a slurry. Stir slurry into chowder base; return to a boil to thicken. DO AHEAD: Base can be made 1 day ahead. Let cool; cover and chill. Keep clams chilled. Bring base to a simmer before continuing.

Remove base from heat. Discard bay leaf. Stir in reserved clams (or two 10-ounce cans baby clams) and cream. Season with salt, if needed (clams' brininess varies), and pepper.

Divide chowder among bowls. Garnish with chives and oyster crackers.