The compositions of nascent planets depend on the compositions of their birth disks. In particular, the elemental compositions of Gas Giant gaseous envelopes depend on the elemental composition of the disk gas from which the envelope is accreted. Previous models demonstrated that sequential freeze-out of O and C-bearing volatiles in disks will result in an supersolar C/O ratios and subsolar C/H ratios in the gas between water and CO snowlines. This result does not take into account, however, the expected grain growth and radial drift of pebbles in disks, and the accompanying re-distribution of volatiles from the outer to the inner disk. Using a toy model we demonstrate that when drift is considered, CO is enhanced between the water and CO snowline, resulting in both supersolar C/O and C/H ratios in the disk gas in the Gas Giant formation zone. This result appears robust to the details of the disk model as long as there is substantial pebble drift across the CO snowline, and the efficiency of CO vapor diffusion is limited. Gas Giants that accrete their gaseous envelopes exterior to the water snowline and do not experience substantial core-envelope mixing, may thus present both superstellar C/O and C/H ratios in their atmospheres. Pebble drift will also affect the nitrogen and noble gas abundances in the planet forming zones, which may explain some of Jupiters peculiar abundance patterns.