Can anything be done for unsightly chest veins? (Photo)

The  veins over your chest can be easily treated with a long pulse 1064 Nd:yag laser such as the Excel V. The older version of this laser is the Gemini which also has a long pulse 532 KTP laser to treat the tiny blood vessels.

It’s important to distinguish between varicose veins and spider veins when choosing between laser therapy, sclerotherapy, and vein surgery. With two board certified vein specialists, our center uses a combination of visual examination, functional flow measurements, ultrasound, transillumination, and infrared light to map out vein networks prior to therapy. Lasers can be used to treat deep varicose vein insufficiency, vein perforators, and varicose veins. Sclerotherapy is ideal for spider veins and reticular veins. Whereas surgery is reserved for severely incompetent varicose vein segments. 
Dr. Karamanoukian
Realself100 Surgeon

Sclerotherapy should work well on these chest veins.  These veins are very common and sclerotherapy is my treatment of choice.

Those veins should respond well to sclerotherapy.  I agree with other posters that a clinical exam and possibly an ultrasound may also be warranted to make sure there are no underlying issues.

Assuming there is no issue with the central veins which return blood to the heart for recirculation, superficial cosmetic veins can usually be treated with sclerotherapy.

On my computer it is hard to see but I would recommend you see your physician and have an evaluation and have an upper extremity ultrasound to make sure there is no underlying cause, first.  If negative some of these can be injected.  They seem to be mainly located on your left side of the chest. 

These can safely be treated by an experienced provider familiar with foam sclerotherapy. There are some technical points to consider, so make sure your provider is comfortable with the breast/chest/trunk area.