Boil some water in a big pot for the pasta. When it starts to boil, add the pasta and some salt. Stir pasta a few times. Cook pasta until al dente, about 11 minutes. At the 6-minute mark, drop the broccoli florets with the pasta and continue cooking for 5 more mins. Save 1/2 cup of pasta water. While pasta is boiling, heat 1 Tbsp of olive oil in a sauté pan or skillet on medium/high heat. Cook the chicken in the pan for 5-6 minutes, turning once, until slightly golden brown.