In a large pot, cook the chopped bacon over medium heat until crispy; remove bacon and set aside, leaving the drippings in the pot.

Add the chopped onion and celery to the pot and sauté until softened, about 5 minutes.

Stir in the diced potatoes and chicken broth; bring to a boil, then reduce heat and simmer until potatoes are tender, about 10-15 minutes.

In a separate small saucepan, melt the butter and whisk in the flour to create a roux; cook for 1-2 minutes until lightly golden.

Gradually whisk the heavy cream and milk into the roux until smooth; cook over medium heat, stirring constantly, until the mixture thickens.

Add the cream mixture to the pot with the potatoes and broth; stir well to combine.

Stir in the drained and chopped clams, salt, and black pepper; heat through for a few minutes, but do not boil.

Serve the clam chowder hot, garnished with the reserved crispy bacon.