The elasticity theory of the twist-grain-boundary phase in chiral smectic liquid crystals for the case of \ensuremath{\alpha} (where 2\ensuremath{\pi}\ensuremath{\alpha} is the twist-grain-boundary angle) irrational is developed. It implies that fluctuations destroy long-ranged translational order, leading to algebraic (rather than \ensuremath{\delta}-function) singularities in the x-ray scattering near both a cylinder in reciprocal space and isolated Bragg peaks along its axis. These results, which could be experimentally tested through high-resolution x-ray scattering, also apply to ``nearly irrational'' \ensuremath{\alpha}=J/s, with J and s integers and s\ensuremath{\gg}1, out to length scales exponentially large in s.