Heat the olive oil in a large, deep frying pan over a medium-high heat. Add the chopped onion and cook, stirring frequently, for 8-10 minutes until soft and any excess liquid has evaporated. Add the chopped garlic and the paprika for the last minute.
Stir through the paella rice, then add the saffron and stock. Bring to the boil, then reduce to a simmer and cook, covered, for 15 minutes. Stir in the peas for the final 2 minutes.
Meanwhile, heat another frying pan over a medium heat, add the chorizo and cook for 3 minutes until browned. Remove with a slotted spoon and set aside. Add the chicken and cook for 10 minutes until golden and cooked through with no pink remaining.
Stir the chicken and chorizo through the paella rice mixture, along with the parsley.