Heat a medium pan over medium-high heat. Add olive oil and chicken and season with salt and pepper. Saute a couple of minutes then add onion and chives and cook another 6 minutes until onions are tender and chicken is cooked through. Turn off heat and reserve.
In a separate pot boil water, add pasta and salt. Cook 5 minutes, then add broccoli and cook 3 minutes more or until pasta is cooked to al dente and the broccoli is just tender.
Meanwhile, heat a large pot over medium heat. Add butter and melt, then add flour, cayenne and garlic and whisk together over heat until it thickens, then cook a minute more. Whisk in milk, heavy cream and stock and raise heat to bring the sauce to a quick boil. Simmer until the sauce thickens about 5 minutes.
Drain macaroni and broccoli florets. Add back to the pot and add chicken to the pasta and broccoli.
Add cheese to milk sauce and stir. Pour sauce over pasta and stir to combine.
Put pasta in a 9 x 13 glass baking pan. Sprinkle with the shredded cheese and broil for 5 minutes.