Given that the chesspub visitors are likely to be males between say 15-50 - it could be a useful place for ads on beer, cars, deodorants
etc. But then they would want to place video clips or interactive things and not only banners.
One solution could be to have a special section only for adverts - people get bored here too, so most of us would take a look and it would be indexed by google so the section would get hits from the outside too.
And while you're at it, why not add another section just for chess related ads? Could be anything from publishers of books, dvds etc to trainers looking for students, teams wanting to recruit new players, players selling off 2nd hand books, dvds etc.
If it's possible, even just a sub-site for selling off chess stuff, with the possibility for auctions could be quite interesting and then you could simply charge a few % from the sales made. The traffic on this site should at least make it worth a try. (something like www . ChessLund . com should definitely be possible, but with a much wider range of chess materials instead of just antique books.)
In short, regardless of the times there are always opportunities to be found or invented, but you must act to make them real. Keeping the site exactly as it is and expect pennies from heaven is not gonna happen. The "downside" is that managing the forum may become a full time job. Something you may not be interested in I suppose, given that you're already restricting new members to the forum...