Long period fiber gratings (LPFGs) formed in photonic crystal fibers (PCFs) are of considerable interest because they can provide many new opportunities for optical and biochemical sensing. LPFGs can be fabricated in PCFs by intense CO2-laser radiation through deforming the fiber geometry or changing the glass structure. In this paper, we report a new, efficient way of writing LPFGs in PCFs, which is based on the generation of frozen-in inelastic tensile stresses in a tensioned PCF by CO2-laser heating. The mechanism, known as frozen-in viscoelasticity, can also improve the writing efficiency of LPFGs in conventional single-mode fibers.