Targeted protein degradation can intervene with the function of disease-related proteins, but most current approaches rely on direct ligand engagement of a protein target, limiting their applicability to proteins that are difficult to bind selectively. We present a conceptually unique approach to degrade proteins associated with DNA G-quadruplex (G4) secondary structures in a chromatin context. G4s are non-canonical nucleic acid structures that form at regulatory regions of transcriptionally active genes in open chromatin, and are abundant in cancer states. While many proteins recognize or regulate G4 structures, selectively targeting G4-binding proteins in their native chromatin environment is challenging. Our bifunctional molecules are PROTACs that bind naturally occurring G4s, recruit E3 ubiquitin ligases and degrade G4-specific transcription factors and chromatin remodelers such as FUS, SMARCA4, and ATRX. These proteins are important therapeutic targets that play crucial roles in transcription regulation and DNA repair. Our approach has the potential to be exploited in a therapeutic strategy to target diseases characterized by aberrant G4 activity, such as cancers.