Cut the beetroot into wedges, transfer to a bowl and cover. Combine the red wine vinegar, sugar and a little seasoning in a small saucepan. Bring to a boil over a moderate heat and continue cooking until you have a thin syrup. Add the beetroot to the saucepan and swirl to coat.
Reduce the heat and cook until warmed through. Spoon the beetroot onto serving plates. Scatter the red onion and feta cheese amongst the beetroot, then sprinkle the chervil leaves around the perimeter of the plates.
Drizzle the sauce from the pan around, then do the same with the olive oil. Season and serve immediately.