No special oil is required. Bike shops sell a range of chain lubricants, all will do a job, some are very much boutique priced. Believe it or not I saw a small bottle of oil on sale for £12! I use light oil, it works well and is widely available, as "cycle oil" or "3 in 1" type oil. I would advise against using car engine oil unless you are desperate, it has additives in it that make it very "sticky". This is ideal in an engine as it means that the oil sticks to the moving parts and doesn't drain off overnight, but on a bike chain it means that the oil picks up every bit of passing debris and adds it to the mix.
A lot here use things like "Finish Line Chain lube" which seems to be well liked and while it's hardly a cheap product it doesn't suffer too much from the "snake oil" claims and boutique pricing of some of the products on the market.