OK, I have searched the site and have not seen this suggested. I HAVE seen the suggestion about the rocket powered chainsaw, but this is a different idea that might be in the realm of possibility.

Everyone has seen the v8 powered chainsaw
http://www.youtube.com/watch?v=60Tamp2fHhg

Can you build a chainsaw powered by a turboshaft engine?

Perhaps one of these numbers

http://www.turbinesbygateway.com/forsale.html

Possible? Yes. Practical? Not so much.

There are several problems with a turbine in such an application.

1. Small turbines like what you would need typically don't start very well on their own. They usually need extra equipment to get them going. That equipment would need to be carried by the operator. You are typically stopping and starting a chainsaw multiple times through the work process.
2. The large amount of hot exhaust gas wold be a safety concern for someone holding the thing.
3. Reaction time. Turbines are great for maintaining a constant speed. However they are rather slow to speed up and slow down. In a chainsaw application, you typically want something that can rev up and down quickly for safety and productivity reasons.
4. Turbines are not overly good on fuel efficiency. They can take quite a bit more fuel to run the same amount of time as an IC engine does. this extra fuel will have to be carried to the operator. extra weight will limit how long an operator is willing to use it.

Right you are, not practical except for its amusement value. I was thinking you would need to build a stand that raises and lowers to put it on that you can operate remotely. Raise it up, position it over the log, let it drop. Maybe you could have the saw pointed up vertically and pull/push the stand into a log. In any case, I wouldn’t want to be any where near this thing.

Not sure if a dry clutch mechanism would help with varying the chain speed. Also, would the chain even hold up to the force.

Since this is obviously a just for the Hell of it kind of thing, this might be easier than the V-8 saw. You might look around for a scrapped aircraft APU. There are also a couple small engines available for someone with a bottomless wallet like the surplus cruise missile engines or this:

Turbine Technologies

There are also turboshaft engines for R/C aircraft that would be a size more portable. Thats if you are wanting to plop down a few thousand dollars for an engine you are putting into a chainsaw.