We explore the possibility that large-scale convection is inhibited over some regions of giant planet interiors, as a consequence of a gradient of composition inherited from either their formation history or particular events like giant impacts or core erosion during their evolution. Under appropriate circumstances, the redistribution of the gradient of molecular weight can lead to double diffusive layered or overstable convection. This leads to much less efficient heat transport and compositional mixing than large-scale adiabatic convection. We show that this process can explain the abnormally large radius of the transit planet HD 209458b and similar objects and may be at play in some giant planets, with short-period planets offering the most favorable conditions. Observational signatures of this transport mechanism are a large radius and a reduced heat flux output compared with uniformly mixed objects. If our suggestion is correct, it bears major consequences on our understanding of giant planet formation, structure and evolution, including possibly our own Jovian planets.