  We study 4$\alpha$ linear-chain states in 16O in comparison with 3$\alpha$
states in 12C by using the Generator Coordinate Method within a microscopic
$N\alpha$-cluster model. It is shown to be very important to solve relative
motion of $\alpha$-clusters by taking into account the orthogonality between
the linear-chain states and other low-lying states including the ground state.
For 12C, the 3$\alpha$ chain state disappears because of this orthogonality.
The $4\alpha$ chain state in 16O, on the other hand, is hardly affected by
low-lying states and persists to remain above the 4$\alpha$ threshold. The
calculated moment of inertia of the $4\alpha$ linear-chain rotational band (88
keV) reproduces the experimentally suggested value qualitatively.

Nuclear Theory