Heat a griddle pan until smoking hot. Brush the chicken fillets with the olive oil, then cook in the griddle pan for 7-8 minutes on each side, or until charred and cooked through.
Meanwhile, combine the ingredients for the pesto in a mini food processor, or with a mortar and pestle. Add 2 tbsp water to loosen.
Cook the tagliatelle according to the instructions on the packet, then put in a large bowl. Slice the cooked chicken into diagonal slices, then toss well with the tagliatelle, pesto and reserved rocket. Divide between 4 bowls to serve, then garnish with the remaining parmesan.