A friend of mine is blind in one eye and has normal vision in the other eye. Would this prevent him from getting a Private Pilots License in the US?
It's possible to get a special issuance medical certificate in this case:
An applicant will be considered monocular when there is only one eye or when the best corrected distant visual acuity in the poorer eye is no better than 20/200. An individual with one eye, or effective visual acuity equivalent to monocular, may be considered for medical certification, any class, through the special issuance section of part 67 (14 CFR 67.401).
It is both perfectly safe and perfectly legal to fly with monocular vision.
Safe: A classic US Air Force study (that led to a revolution in the study of vision and neuroscience more broadly) demonstrated many decades ago that (a) our sense of depth comes from many sources, and (b) stereo is of remarkably limited utility in many situations -- for example, when objects are much further away than the distance between our eyes, as is the case in most situations while flying. Motion is in many cases far more important. This is extremely well established in the literature.
Legal: as mentioned in a previous answer, monocular pilots require a special waiver for their medical certification. The reason is simple: monocular vision, by itself, is not a biggie; but if you have one eye, it's worth making sure there's nothing else amiss, and that a pilot with recent loss of vision has developed the intuition required to comfortably sense depth with other cues.
Tell your friend to go do it!
Just an addition to the previous answer,
While they may be legally able to get a medical cert and complete the training they may find it extremely difficult. Having vision in only one eye can have a drastic impact on depth perception and ones ability to observe motion. The human body can see distance, and motion (distance change over time) largely by triangulating objects from both eyes. If the loss in vision happened later in life many people are able to retain enough estimation ability to still be able to see and estimate motion and distance with ease. While I would advise him to give it a try he may find certain things very difficult and he should be prepared for that. I would also strongly advise an instrument rating in this case so as not to need to rely on vision all the time.