Likely a hose running to a vent would be my guess.

There was a short piece of hose with a special screw on the other end on that fitting. As Tom suggests, the screw allowed air in to replace the fuel used.

I had the saw out this afternoon to cut up a tree that came down in the wind. It starts and runs but has no guts. I can't get it to rev up to full speed and it stalls as soon as begin I cutting. Could this missing hose/vent be the problem. I have not had a chance to check the fuel filter in the tank yet. Is there a filter in the tank? Is there a filter in the carburetor that might be clogged? My old Remington had a screen in the carb that I needed to clean every so often.
Here is a photo. You can see the fitting right above the fuel cap.

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There is a filter in the tank on the end of the hose and they both likely needs replacing. That is an old saw and has likely been sitting unused for some time. The carburetor probably needs an overhaul, this should be left to an experienced tech as this paticular model is prone to air leaks.

The filter in the tank is good. I checked it this morning. The saw has not been sitting. My brother used it regular. He gave it to me when he got new Stihl 026.

That is a fine looking saw. Have you ever done a compression test? From what you say, you might be lucky enough to pull the muffler/ cover clean up the exhaust, grab a new air filter, put the vent on and try fine tuning the carb a bit. Take some jet spray gumout once it's at idle and spray it around the intake, throttle shafts etc. If it picks up speed, it is sucking air as canguy suggests. It wouldn't be a bad idea to spray the carb off a bit first. It may need the fuel system redone after all, but start with the easy stuff and see how it goes.