Your question is confusing because you say "create" when you probably mean "host."
You certainly do not need to develop your own. You can set up one of many available XMPP servers, a fairly extensive list is here. There are both commercial products and open source ones.
There are also many publicly available ones that you can use. Two of the more popular today would be Google's gtalk and Facebook chat.
Your own use case is what really determines which path you should take. For publicly available servers all the users would have to be registered with those domains to use them.