Eagles: Their Greatest Hits 1971-1975 (Vinyl LP)Their Greatest Hits (19711975) is the first compilation album by the American rock band the Eagles, released by Asylum Records on February 17, 1976. It contains a selection of songs from the band's first four albums, which were released from 1972 to 1975. On the U. S. Billboard 200 chart, the album reached number one, where it stayed for five weeks. The album has the distinction of being the first album to receive the RIAA's Platinum certification,