Preheat the oven to 180°C. Toss the tomatoes in the oil, then put them in a roasting tin and bake for 12–15 minutes.
Meanwhile, lay out the veal pieces between two sheets of plastic wrap. Using a meat mallet or heavy rolling pin, pound the veal to flatten it – this will help it cook evenly.
Heat the butter in a frying pan until it starts to foam, add the veal and cook over a moderate heat for 2 minutes on each side, or until tender. (Depending on the size of your pan, you may need to do this in two batches.) Remove from the pan and set aside in a warm place.
Pour the balsamic vinegar into the pan, stir into the buttery juices, then bring to boil. Cook the sauce over a high heat for 5 minutes, or until the sauce has reduced by half.
Return the veal to the pan briefly to reheat it, then sprinkle with the chives before serving with the cherry tomatoes.