Cook the pasta in a large pan of boiling water for 3 minutes.
Meanwhile, heat the olive oil in a small pan and cook the chilli for 2-3 minutes until softened. Add the lemon zest, crabmeat and a ladleful of water from the pasta pan. Season with freshly ground black pepper and heat gently until the crabmeat is piping hot.
Drain the pasta well and return to its pan. Add the crab mixture (reserving some to place on top), basil leaves, and lemon juice to taste. Toss well, divide between 4 bowls, top with the remaining crab meat and serve immediately.