We Kill Servers :: Cloud/cluster

Our website is based around a customer based chat system. Customers are only on the system during a particular day and time range. So for parts of the week the server gets almost no traffic. When then time for a chat comes up we get hundreds of people on the site all doing page requests every few seconds.

So as you might imagine we are bringing the server to it's knees with heavy CPU and memory loads. Plus bandwidth usage is really high. We are currently on the biggest box that Rackspace has to offer. The site runs ok on it during these times. It's a little slow but not unbearable.

But we have not hit our max customer base. In fact if all goes well we will double our customer base next month. So I know when we do we will bring that box down totally.

I was thinking about possibly trying a cloud/cluster based approach but after some research on this site I have found that is probably not the best option.

So I am looking for advice on what to do? Is there a better host? Different technology?

Servers are not my thing really so I could really use some help.

No we can't change the way customers access the site or when they access. There is nothing that can be done in that regard so don't suggest it.