Chain not getting oil

Extremely difficult! If the oil pump or worm gear is defective it may be the most difficult saw to repair. This is the only saw I have seen with the oiler mounted behind the fly wheel.

Your basic model number is 600035. There are 11-, 21-, and 22- prefixes used with 600035s. There are also a ton of suffixes with the 600035s. I think the suffix is on your saw immediately after the basic model number somewhere (usually on bottom of older Macs along with the serial number. The dash of the serial on older Macs is the prefix). I must defer to you to find your exact IPL, here:
McCulloch IPLs
http://www.ordertree.com/modelinfo/McCulloch/139.59.html

I chose this one as an example "22-600035-58" for an IPL
http://www.ordertree.com/modelinfo/MCC/22-600035-58-Mac-3516-IPL-211229-01/139.22-600035-58-Mac-3516-IPL-211229-01.1.59.1.html
The "Powerhead Assembly" lists an oil pump (1) and a worm gear (10). These are the most common failure on most saws but Macs have many more hoses than most. There are oiler components on at least 2 different details. It appears the oil pump is on the starter side of the engine. and you may need to remove the fly wheel for access. I would examine every connection and perhaps try the "Kit Gear/Plunger Assembly" before trying to access the oil pump and gear.

Oil System Plugged.

1. Remove the clutch cover, bar, and chain, clean the bar groove, any holes and passages on the rear of the bar (both sides, consider rotating the bar), if equipped with a sprocket nose ensure it rotates easily at least one complete revolution. Clean the saw oiler hole and channel. Insert a blunted, hooked piece of wire through the oil filler hole and pull the hose in the oil tank out. Pay attention to the screen or filter on the free end (clean or replace, difficult to determine serviceability). Start the saw and see if it oils when revved up. If yes reassemble your saw. If no, continue with 2.
2. Work your way through the linkage cleaning and replacing any defective parts as you go. Carefully check the hoses for cracks especially at bends and connections. Please make extensive notes & some digital pictures will help during reassembly.