Cook penne according to packet instructions. Drain, and transfer to a large bowl.
Heat 1 tablespoon of the olive oil in a large frying pan over medium heat. Cook chicken until firm and lightly browned; remove from pan.
Add the remaining tablespoon of olive oil to the frying pan. Gently cook garlic, asparagus and crushed chillies in oil until asparagus is tender. Stir in chicken, and cook for 2 minutes to blend the flavours. Season with salt and pepper.
Toss pasta with chicken and asparagus mixture. Sprinkle with parmesan.