Bring salted water to a boil in a large pot. Add pasta and cook according to package directions. Meanwhile, cut chicken fillets into thin strips. Heat clarified butter in a large pan over medium-high heat. Fry chicken, stirring often, until golden and cooked through (about 5-6 minutes, internal temperature 74°C / 165°F).
Peel and dice the onions, then add to the chicken. Cook for 2 minutes. Season with salt and pepper. Sprinkle flour over and cook for 1-2 minutes, stirring. Stir in tomato paste, pour in broth, and simmer for 5 minutes. Remove from heat and stir in crème fraîche.
Cut chives into small pieces. Drain pasta and divide among serving plates or bowls. Spoon chicken ragout over pasta. Top with chives and serve immediately.