Heat 1 Tablespoon olive oil in a large, heavy-bottomed pot over medium-low heat. Add 3 leeks and 2 minced garlics and sauté them for 2 minutes.
Add 1 cubed potato, ½ cup chopped celery, ¾ teaspoon salt, and ¾ teaspoon pepper and cook over medium heat for about 1 minute, stirring constantly.
Add 3 cups broth, cover and simmer for 10 minutes. Remove lid and continue to simmer until potato is tender, about 5 minutes more.
Add 3 Tablespoons tomato paste and 3 cups milk, and 8 ounces salmon, reserving a few flakes to decorate top of soup. Continue to heat soup for a few minutes but don't let it come to a boil or the milk will separate.
As the chowder heats, stir in ¾ cup cream and continue to heat through.
Remove from heat, garnish with chives, crack more pepper over the top, and serve.
This soup is still delicious one and even two days later which is not always the case with fish recipes.