Combine the oil with the remaining ingredients and a little salt. Coat the chicken breasts with the mixture.
Slice off the top and bottom of the oranges, then peel all round the fruit down to the flesh. Cut the oranges into slices, arrange in the roasting tin. Add the chicken breasts. Scatter the dates and pistachios over the top.
Roast for approx. 25 mins. in the centre of an oven preheated to 200°C.
Carve the chicken breasts and serve with the oranges.