Preheat the oven to 350°F and place 2 wire racks on the upper and lower thirds. Put the oil in the bottom of 2 shallow roasting tins (I used jelly roll baking trays), about 1 1/2 tablespoons in each. Rub the skin of the chicken in the oil, season with salt accordingly, then turn them skin-side up, 6 pieces in each tin. Divide the chorizo sausages and the new potatoes between the 2 tins.
Sprinkle the onion and the oregano over, then grate the orange zest over the arranged contents of the 2 tins. Cook for 30 minutes, then swap the top tray with the bottom tray in the oven and baste the contents with the orange-colored juices. Continue cooking for about 30 minutes or till chicken is done.