Measure out and reserve 1 cup (250 mL) of clam liquid from canned clams. Also, reserve drained clams.
Melt butter in medium saucepan set over medium heat. Stir in carrot, celery, onion and dill; cook 5 to 7 min. until vegetables start to soften. Sprinkle with flour. Cook, stirring, 2 min. Slowly whisk in reserved 1 cup (250 mL) clam liquid until sauce is smooth. Add vegetable broth. Whisking, bring to a boil. Add potatoes. Reduce heat to medium-low and cook, covered, 12 to 15 min. until potatoes are tender.
Mix in reserved clams, milk and pepper; bring to a simmer 5 to 7 min. Stir in chives just before serving.
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