By accident ran across a review of supplemental chambers in the 5th ed. Gun Digest Treasury.  A Marbles chamber tested in a .30-30 produced 3-shot groups of 1" at 25 yds.; but as the author stated, hitting a grouse at that range was all that was expected.  Best of the devices appeared to be one made by RWS similar to the Marbles with its own spring-loaded firing pin.  

I live where there are fair grouse populations, and a few times I've encountered one that loitered long enough to make itself a good target, assuming the chamber was loaded and ready to fire.  But 99% of them flush without my even seeing them, so instead of a supplemental chamber, a can of sardines might be the hunter's wiser choice.