I think that SAWStudio and Samplitude do this, but I'm not sure. I know that both offer a 'strip silence' feature, but I'm not sure about the 'save' options, if you have a choice to save each then created chunk as it's own file, or if you are stuck saving it as one long file with the silence removed, or if there are multiple steps in the process.
"I believe that entertainment can aspire to be art, and can become art, but if you set out to make art you're an idiot."
Show business: we're all here because we're not all there.
Resistance is not futile. It is voltage divided by current.