Warm a large pot over medium heat, then cook the chopped bacon until it turns crisp, stirring from time to time. The bacon should be browned and the pot should hold a layer of fragrant rendered fat.
Lift the crisp bacon onto paper towels and leave the drippings in the pot. Keeping the bacon aside protects its crunch until the chowder is nearly finished.
Add the onion, carrots, and celery, season with salt and pepper, and cook for 6 to 8 minutes. Stir occasionally until the vegetables look softened and the onion loses its raw edge.
Stir in the garlic and cook for 30 seconds. The garlic should smell aromatic without turning dark or sticking to the pot.
Add the tomato paste, thyme, bay leaf, clam juice, chicken broth, and potatoes, then stir and bring the liquid to a simmer. The tomato paste will dissolve into the broth and give it a richer brick-red color.
Maintain a steady simmer for 10 to 15 minutes until the potatoes are tender. A fork should slide through a potato cube easily, while the cube still holds its shape.
Fold in the undrained diced tomatoes and drained baby clams, then adjust the salt and pepper. Keep the heat gentle so small bubbles rise without the chowder boiling hard.
Simmer for 5 minutes, then stir in the reserved bacon and finish with parsley. The clams should be warmed through and tender, with the bacon still providing a little chew.