(Corrects paragraph 1 to say S&P 500 opened “near” an all-time high, not “at”) June 30 (Reuters) - The S&P 500 opened near an all-time high on Wednesday as data showed U.S. private payrolls increased solidly in June, while the major U.S. stock averages look to wrap up their fifth straight quarter of gains. The Dow Jones Industrial Average fell 1.55 points at the open to 34,290.74. The S&P 500 opened lower by 1.15 points, or 0.03%, at 4,290.65, while the Nasdaq Composite dropped 18.48 points, or 0.13%, to 14,509.85 at the opening bell. (Reporting by Medha Singh in Bengaluru; Editing by Maju Samuel) Our Standards: The Thomson Reuters Trust Principles.