In large pot of boiling salted water set over medium-high heat, cook pasta according to package directions.
Meanwhile, in bowl, combine Cheddar, Gruyère and Parmesan. Reserve 1 cup (250 mL); set aside.
In large skillet set over medium-heat, bring cream and garlic to boil. Reduce heat to medium-low; cook, stirring frequently for 10 to 15 minutes or until slightly reduced. Stir in cheese mixture until melted; stir in crab meat, half of the chives, salt and pepper. Toss with pasta.
Preheat broiler to High. Transfer pasta mixture to greased 9-inch (23 cm) square glass baking dish. Sprinkle with reserved cheese.
Broil for 2 to 3 minutes or until cheese is browned and bubbly. Top with remaining chives.
Leftover crab can be used for crab cakes or arranged over a salad.
Extra cream or cheese sauce can be used on pasta or as a fondue starter.
Substitute faux crab meat, or surimi, if desired.
This dish is also delicious made with chicken or pancetta instead of crab.