Excessive inflammation often impedes the healing of chronic wounds. Scavenging of chemokines by multiarmed poly(ethylene glycol)‐glycosaminoglycan (starPEG‐GAG) hydrogels has recently been shown to support regeneration in a diabetic mouse chronic skin wound model. Herein, a textile‐starPEG‐GAG composite wound contact layer (WCL) capable of selectively sequestering pro‐inflammatory chemokines is reported. Systematic variation of the local and integral charge densities of the starPEG‐GAG hydrogel component allows for tailoring its affinity profile for biomolecular signals of the wound milieu. The composite WCL is subsequently tested in a large animal (porcine) model of human wound healing disorders. Dampening excessive inflammatory signals without affecting the levels of pro‐regenerative growth factors, the starPEG‐GAG hydrogel‐based WCL treatment induced healing with increased granulation tissue formation, angiogenesis, and deposition of connective tissue (collagen fibers). Thus, this biomaterials technology expands the scope of a new anti‐inflammatory therapy toward clinical use.