Simple renewable furans can be used to derive various monomer structures for use in polymeric materials. The dimethyl esters of 2,5-furandicarboxylic acid (FDCA), 5,5′-thiodi(2-furoic acid), and 5,5′-sulfonyldi(2-furoic acid) were reacted with diethylene glycol, yielding renewable polyesters with excellent O2 barrier properties and facile chemical recyclability. Glass transition temperatures for the polyesters were 33-70 °C, while thermal decomposition took place at 321 °C or above. Oxygen permeabilities were measured from free-standing films and compared to poly(ethylene terephthalate). The polyesters showed excellent barrier improvement factors (BIFs) of 3.1-6.0 and 5.2-11.0 at 50 and 0% relative humidities, respectively, with the polyester from the sulfide having the highest BIFs, followed by the polyesters of FDCA and the sulfone in an order that depended on humidity. The three polyesters were remarkably easy to chemically recycle under mild conditions. The original dimethyl esters were recovered by filtration after a room temperature reaction with anhydrous methanol and catalytic K2CO3. Monomer yields from film recycling reached as high as 96% for the sulfide-based polyester with high purity.