What motorcycle part is this?

Just try cleaning it and tighten up if that don't work replace it

Oil return line to the sump. Replace it and get a new clamp.

It is a rubber hose held on with a clamp.  Replace both as the rubber aint rubber anymore. She is cooked hard. New clamp too. It has a reason for existing. I don't own a Harley.

are you talking about that black oil line? Pull it off. Clean the metal tube it hooks up to. Replace the clamp. Its no longer holding tight enough. Or your leak is a bad gasket . Pull the case cover off . Clean both surfaces. Replace the gasket. 

My FX had a leak from the primary drain plug. I haven't had a Sporty in years (a '75) so I Guess that might be your problem, also. 

Picture isn't clear, I don't remember  an  oil line there on mine. My FX is a wet sump

If there is a clamp on that hose, tighten or replace it. If no clamp, might wanna put  an Ideal clamp on it.  . Snug down the primary screws, too. If you are stumped, get some of that dye they sell at AutoZone, put a little in primary, first.  Oil can run Down or be blown back from its source--a pan leak on my cage went all over  transaxle and exhausts.  I thought it was rear mains until I took it down. 

@adam, that looks more like a breather line. Still can cause drips, of course.

Could just be oil leaking from the crankcase gasket.