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To obtain an O-1 visa you have to prove your extraordinary ability. Most of the people obtaining O-1 visas are those who went through fellowship, did some research, etc. You need to provide several letters of recommendation from different institutions from people who know you. These letters should be speaking of you as of an expert in the particular field. You also need to show other accomplishments such as publications, awards, membership in organizations. The more you can find, the better. The requirements are similar to the applicants for a green card through "extraordinary ability", but probably less strict, because I got an O-1 and not GC.