Halocho #945 - What happens if your Chanukah candles blow out?

A Chanukah Menorah must be lit such that it could burn for the required half hour.

If it didn't have enough oil, or the location was windy, then one has not fulfilled the Mitzva, and one must fix the problem and light them again. No Bracha is said the second time.

If it was not a windy place, and it unexpectedly blew out, the Mitzva has been fulfilled, though the Minhag is to light it again.

One cannot light one candle from another; one needs to use the Shamash or another source of fire.

Source: Kitzur Shulchan Aruch 139:1

- Danny
Tuesday, 17 Kislev 5772