Imagine that there are two really strong computers that try to find an address starting with
1ABCDEFGH. Is there a possibility does that two computer find the same private key?
You have enough entropy in Bitcoin private keys to make this possibility extremely unlikely (just like with non-vanity address).
A nice chapter on vanity addresses (their generation, security etc) can be found at: http://chimera.labs.oreilly.com/books/1234000001802/ch04.html#_vanity_addresses.
Theres a possibility, its still unlikely.
heres a couple of attempts. Not quite as many characters since it will take to long.
Case sensitive will take longer.
http://directory.io/ has a list of all bitcoin public/private keys
still looking for an atom in the galaxy.