Cook the pasta according to the pack (usually 3-4 minutes in boiling water). Add the peas for the final 2 minutes of cooking time. Drain and rinse with cold water to cool, then drain again.
Chop the parsley and snip the chives into a large mixing bowl. Add the zest and the juice of the lemon to the bowl, then add the olive oil and the cooled pasta and peas, with plenty of salt and freshly ground black pepper and mix well. Cover and chill before serving.