Preheat the oven to 350 degrees F.
Toss the carrots and parsnips with olive oil, salt, the honey and cayenne. Put them on a sheet tray and roast for 20 to 25 minutes.
Toss the radicchio with olive oil and salt and place on a small sheet tray. Add to the oven with the carrots and parsnips for 10 minutes.
Combine the carrots, parsnips and radicchio and toss with the chives. Serve hot or at room temperature.