Reddit mentions of Castrol 17306540 400ml Chain Lube Racing Oil

I'm gonna play devil's advocate and say it's not uncommon for the first chain on a 125 to be neglected. I've done it, learned from it and my chains have never been better because of it. The amount of slack that can be pulled off the sprocket is not something that can be tightened. The amount of slack there shows the rollers are worn from abuse and not the garage's fault. To explain this better, the rollers are secured at the 12 and 6oclock position on the rear sprocket, they cannot slide about. The worn pins under the rollers increase the chain length, thus you can pull it off the chain. A good chain will not be worn and you cannot pull it off the chain.

What is important is how much freeplay there was between the 2 sprockets and this is what tells you if the garage did anything. If THAT is 1 inch at the tightest point then they did adjust it. As you have said your chain has multiple tight spots that says your chain is near end of life. Do not tighten it more than 1 inch of freeplay at its tightest spot as you'll damage your gearbox!

That chain was neglected by the previous owner so as a treat to your new chain, get some good chain cleaner ; a chain brush and some lube. Also if you have the budget, some Scott towels because they're really good. You can make it last 15K miles easily if you clean it regularly (600 miles normally, 100 in winter).

I'm not sure how much you know about cleaning chains but for your future benfit, you degrease it with cleaners, agitate it with a brush, wait then wash it all off and thoroughly dry it (I use scott towels as they're super strong and it'll get very dirty). Then sparingly apply the lube on the inside of the chain, between the rollers and the links.

Chain will last so long everyone will be amazed. You'll show your buddies who will marvel at how shiny your 20K mile chain is. You'll realise you can charge them a pound every time they look. Soon you'll have set up your own travelling sideshow as your 30K mile chain is still on there. After travelling Britain you'll return home, the adjusters being right at the limit. You'll have finally come full circle as you replace the chain with all the money you earned from your sideshow.