Heat the olive oil in a large, heavy-bottomed pot over medium-low heat. Add the leeks and garlic and saute them for 2 minutes.
Add the potato, celery, salt, and pepper and cook over medium heat for about 1 minute, stirring constantly.
Add the broth, cover and simmer for 10 minutes. Remove lid and continue to simmer until potato is tender, about 5 minutes more.
Add the tomato paste and milk, then the 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 the 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.
Cook's note: This chowder is delicious with asparagus tips added in at the same time as the tomato paste and milk. I add about 1 cup.