While the introduction of polymers in aerogels strongly enhances their toughness, truly elastic monolithic aerogels able to restore their dimensions upon extensive compression are still challenging to synthesize. In this context hydrophobic semi-crystalline polymers with low glass transition temperatures that combine both stiffness and flexibility have only recently gained attention. We show that polyethylene aerogels with low density combining chemical crosslinking and high crystallinity display high moduli and excellent mechanical resilience. In order to maximize the crystallinity of these aerogels while maintaining a high crosslinking density, we synthesized polyethylene networks with well-defined segments by hydrosilylation-crosslinking of telechelic, vinyl-functionalized oligomers obtained from recent advances in catalyzed chain growth polymerization. Recoverable deformations both above and below the melting temperature of polyethylene affords remarkable shape-memory properties.