Coolant leak

Are you sure it is oil? If the coolant system has been exposed to air from a bad radiator cap or the coolant has never been serviced it can get a brown "goo" that looks like oil.

If however you are sure it is an oil, what color is it. If red in color it is a bad transmission cooler, located in the radiator. For that you will want to check the transmission fluid to see if it has coolant in it. If it does get a flush done and hope it was caught in time, coolant does bad things in a transmission.

Also you will need to change the radiator and flush the cooling system with a good detergent flush to remove the oil. Then re-fill with fresh dexcool.

If the oil is a dark color you should start with a pressure test on the cooling system. There are very limited ways that oil can get into the coolant. A bad head gasket is one. A pressure test would give you an idea of the issue.

If so you will want to check the transmission fluid for contamination ASAP. Then do the flush and replacement of the radiator.
And as you will have it apart I would add in a second trans cooler, heat is a big enemy of transmissions. Extra cooling is easy and a lot cheaper than a burnt transmission.