I have a 2006 Suzuki Drz400sm (if that's important). My chain was too long and slowly ate a tiny hole in my motor. Im just wondering how much the labor should be roughly to have the engine removed, the hole welded, and the engine put back in? Also what parts will need to be replaced and how much will they costs?

If the hole is in the engine case... the cost can be significant... because the engine cases would have to be completely disassembled... degreased... heated and TIG welded by a professional experiences in welding cast aluminum engine parts. Sometimes further machining is needed.

The engine would have to be completely reassembled with new gaskets and reinstalled.

THere is a LOT of labor involved. And not something just any welder can do correctly....and not all welders are mechanics as well.

Costs are likely in the thousands....and depending on what type this is...it can vary by thousands from one bike to the next.

I should have specified where the damage is. Luckily the damage is on the outside, and appears to be an easy fix. Any idea what this should cost in this situation?

Outside of what exactly (this is important)... if its on the outside why would the engine need removed? You simply remove the damaged cover but in some cases its cheaper to get a used or new cover than it is to have it welded.

But on every bike I have owned... except for the sprocket cover, or the engine cover in front of that... anything else has been the actual engine case. Which you would have the situation I described.

Very few bikes have separate engines and transmissions... the rest have integrated units. So it would help to know what make and model motorcycle this is.

Since you did not mention the loss of oil, what was the cover with the hole in it covering? You might have lucked out and only have a cosmetic problem.