The chimney would have to become part of the interior space of the house; in other words, remove the wall on either side
enough to allow air to circulate around the chimney, then build out an addition and glass in the chimney. And you'd need to have the right amount of sunshine to be able to heat up a huge thermal mass, as chimneys are big and heavy. It's an intriguing idea. I'm not sure if the sun would add a lot of calories to a mass you are already heating up with a stove, but maybe it would. It would probably cost about $5000-10,000 to do if you hired someone, which would buy a lot of heating oil. So I'm not sure that the embedded
energy would pencil out. But it might, in the right (cold sunny) climate.