Right or wrong, a hosting company may face several reasons:
1) The odds are good, they use preprock. Each chat request is likely to be a new connection and thus take off one Apache process. Each apache process is powered from 1 mb of memory to 100 mb of memory.
2) If they support the database server, and you, the client, suck when programming the database, you can clog their database. "Suck" means anything from "without proper indexing" to "makes a few simple queries, not nice thick ones."
As suggested above, make sure your code uses persistent connections. Also:
1) Implement a debugging algorithm on the client. Polling the server once per second during activity, then shutting down for up to five seconds, then ten, twenty, etc. Thus, you do not clog the server when there is no activity.
2) Several tabs will kill you. The user opens 10 tabs, and all of them have a chat widget, polling the server once a second? Bad news. Even if your host does not get angry, your performance will degrade.
If this thing gets huge, design your system so that you can run the chat server bit regardless of the rest of your web application. In other words, customers will make a request to "chat.yourwebapp.com", which, in turn, works on something like lighttpd.
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