Is it possible to remove a large blue vein on my face (side)? (photo)

This can typically be improved with a long pulsed yag laser , I would avoid sclerotherapy.  Best, Dr. Emer.

This is a common problem and is seen routinely in large vein practices such as ours. Given the picture you provided, sclerotherapy would be the best option. Vein specialists who have taken care of these will tell you up front that it will take MORE than 1 session of sclerotherapy to take care of such veins. It is not likely that 1 session will eliminate this vein on the face. Good luck and hope you find someone who has some experience doing sclerotherapy on facial veins. When you discuss pricing with the physician, make sure you discuss up front if the treatment cost is for 1 session, 2 sessions or 3 sessions. 

The first thing you
need to do is to consult with a board-certified dermatologist or plastic
surgeon who is an expert in laser therapy. This kind of vein is not normally
treated with sclerotherapy, as there are too many risks with this treatment in
this area. Laser therapy works really well, with a skilled provider, and the
1064 nm Nd: YAG laser is the best bet here.

Prominent veins on the face can be treated by Sclerotherapy - usually one treatment is sufficient to permanently remove such veins.  This is how I routinely treat these veins.  Although laser* is often used for these veins, it is not consistently effective - usually the veins persist, especially after one treatment.[*The laser that is used most often is a long-pulsed 1064nm (Nd:YAG) - this is different than the short-pulsed 1064nm (Nd:YAG) used to treat tattoos.]David Green, M.D., F.A.A.DDermatology & Phlebology, Bethesda, MD 

This vein can best be treated by sclerotherapy.  It may require several sessions. Laser is also an option but my procedure of choice is sclerotherapy.

I believe YAG laser treatment are a good choice and I would feel more comfortable with this than sclerotherapy.Stephen M. Davis, MD, FACSGreen Hills Plastic Surgery

Yes, it can be treated with injection sclerotherapy or laser.I have had good results with both.Which treatment is used depends on size of vein,location, and individual experience.