Why does one light on a new chandelier light up after the others?
Your chandelier uses compact fluorescent lamp (CFL) bulbs. Unlike conventional incandescent bulbs, these devices have internal circuitry that causes the bulb to light. CFL bulbs have been noted to take some time to come on and to reach normal brightness as the circuitry reaches full activity. 

More recent versions of these bulbs have improved and are often advertised as instant on. However, there may still be a slight delay. This is normal. If you swap the delaying bulb into a different socket, it is likely that the new socket will now show the slight delay.

If you try other bulbs (or other brands), you may be able to find ones that come on simultaneously.