We present a new picture that the α-linear-chain structure for 12C and 16O has one-dimensional α condensate character. The wave functions of linear-chain states that are described by superposing a large number of Brink wave functions have extremely large overlaps of nearly 100% with single Tohsaki-Horiuchi-Schuck-Röpke wave functions, which were proposed to describe the α condensed "gaslike" states. Although this new picture is different from the conventional idea of the spatial localization of α clusters, the density distributions are shown to have localized α clusters due to the inter-α Pauli repulsion.