Eric Schmidt spreading word of an Android-based Google tablet, HP building one as well?

According to a report by The New York Times, Google's apparently looking to get into the tablet game itself. Eric Schmidt was reportedly talking up the device at a party in LA recently, saying that it would run Android exclusively -- which seems odd given that Google has been working on Chrome (a concept Chrome tablet is pictured above), but then again, we don't attend parties in LA so what do we know? Other people with "direct knowledge" of the project say Google is also hunting down publishers, operating in a "stealth mode." NY Times is also reporting that HP will be building another tablet outside the Slate, which will also run Android and has been nicknamed "the half-pint" for its 6-inch screen size (and, presumably, a feisty spirit / heart of gold). We're still unconvinced that Android is exactly appropriate for a tablet device, but if Google is indeed building its own, we're guessing we could see some tablet-friendlier software that could make Android into a true tablet contender -- how 'bout starting with the browser, Google?