Cook pasta according to package directions. Drain and set aside.
Meanwhile, heat the oil in a large deep skillet over medium-high heat. Add the chicken and cook for 3-5 minutes, until golden all over. Add artichokes, tomatoes, cream, and pesto. Bring to a simmer and stir frequently for 3 minutes, or until the chicken is cooked through.
Fold in the cooked pasta and parmesan cheese. Cook 1 minute longer to heat through. Add more cream if neneed to thin out sauce. Season to taste with salt and pepper and serve.