Place the olive oil in a large heavy-bottomed pot over medium heat and saute the pieces of chicken until golden brown on all sides, about 12 minutes. Remove the chicken pieces with a slotted spoon. Add the onions to the pot, along with the red pepper flakes, and cook them for 10 minutes or until translucent. Add the tomato and the tomato paste, mixing well. Add the saffron and allow to simmer for 3 to 4 minutes. Add the chicken back to the pot, along with the basil, and lower the heat, allowing the sauce to simmer for 30 minutes. Season with salt and pepper.
While the chicken is simmering, cook the pasta, drain it, mix well with the sauce and serve with the grated Pecorino on the side.