Preheat the griller to medium-high. Trim the chicory and cut the heads in half, lengthways.
Put the chicory halves on the griller rack, cut side down, brush with half the olive oil and grill for 5 minutes, about 10cm from the heat. Turn the chicory, brush with the remaining oil, and grill for a further 3 minutes, or until the edges begin to char.
Meanwhile, make the dressing. Squeeze 1 tablespoon juice from the orange and stir into the mayonnaise, then stir in the wholegrain mustard.
Remove the chicory from the griller. Arrange, cut side up, in a serving bowl with the beetroot alongside. Drizzle the orange and mustard dressing over the top and garnish with the chives, if using.