Toss the potatoes with 2 tablespoons of the oil and place in a large, shallow roasting tin. Place in a preheated oven, 200°C (400°F), Gas Mark 6, for 5 minutes, then arrange the chicken breasts on top and drizzle over a little more oil. Season well and return to the oven for a further 10 minutes.
Arrange the asparagus spears in the tin, pour over any remaining oil and return to the oven for a further 5 minutes until golden and cooked through.
To make the gremolata, mix together the garlic, lemon rind and parsley. Scatter over the chicken and vegetables before serving.