As suggested in an answer to the earlier meta question about site promotion, one method is to craft a site promotion ad for use on already graduated SE sites. So the purpose of this question, which I based directly on the analogous one at mathematica.SE, is to solicit potential ads which are designed to promote chess.SE on more established SE sites.
Each graduated SE site has a meta question where people can submit these ads (here is the one at physics.SE, for instance), and if they receive enough upvotes they will be automatically shown by the system on that site. If we get consensus on something good here, then we can submit it to the community promotion ad questions on other sites for potential use.
When an actual community ad is submitted, it is required to be in a particular form (detailed in the mathematica.SE question linked to above). In particular, the image must be exactly 220x250 pixels, in GIF or PNG format (not animated), and hosted on SE's Imgur account. It's not strictly necessary for answers to this question to follow that format, but it would be convenient. Answers posted here should definitely include the three required elements: image, tagline, and URL.