The purine rich oligodeoxyribonucleotides 1C, d(ATGACGGAATA) and 2C, d(ATGAGCGAATA) alone exhibit highly cooperative melting transitions. Analysis of the concentration dependence of melting, and electrophoretic studies indicate that these oligomers can form an unusual purine rich offset double helix. The unusual duplex is predicted to contain four A.T, two G.C, and four G.A mismatch base pairs as well as a single A base stacked on the 3' end of each chain of the helix. Other possible models for the duplex are unlikely because they are predicted to contain many base pairs of low stability. Changing the central sequence to CGG or GGG should destabilize the duplex and this is observed. The unusual duplex of 2C is more stable than the duplex of 1C indicating that the stability of G.A base pairs is quite sensitive to the surrounding sequence. Addition of 1C and 2C to their complementary pyrimidine strands results in normal duplexes of similar stability. We feel that the unusual duplexes are significantly stabilized by the intrinsic stacking tendency of purine bases.