Cook rigatoni in a large pot of rapidly boiling salted water until al dente, about 8 minutes. Drain well in a colander, shaking vigorously. Cool on an oiled cookie sheet or clean countertop until nearly dry and toss with 1 tablespoon olive oil to coat. Reserve.
Puree chicken, fennel, and egg white in a food processor until smooth, about 2 minutes. Transfer to a bowl nested inside a larger bowl half-filled with iced water. Stir until evenly chilled.
Add cream, a 1/4 cup at a time, stirring vigorously with a wooden spoon after each addition, until all is added. Stir in salt, pepper, and hot sauce. (At this stage, the stuffing can be stored in refrigerator up to 24 hours.)
To stuff rigatoni, fill a pastry bag fitted with a #4 plain tip with chicken mixture and stuff rigatoni from both ends. Reserve.
Preheat oven to 400 degrees F.
To make sauce, combine cream, Parmesan cheese, salt, and pepper in a medium ovenproof skillet. Bring to a boil. Add stuffed rigatoni, return to a boil, then transfer to oven. Bake until sauce is thick and bubbly, and rigatoni is cooked through, about 10 minutes.
Spoon into serving bowls or plates, sprinkle with chives, and serve hot.