Triple-negative breast cancer (TNBC) is highly aggressive with a poor clinical prognosis and no targeted therapy. The c-Myc protein is a master transcription factor and a potential therapeutic target for TNBC. In this study, we develop a PROTAC (PROteolysis TArgeting Chimera) based on TNA (threose nucleic acid) and DNA that effectively targets and degrades c-Myc. The TNA aptamer is selected in vitro to bind the c-Myc/Max heterodimer and appended to the E-box DNA sequence to create a high-affinity, biologically stable bivalent binder. The TNA-E box-pomalidomide (TEP) conjugate specifically degrades endogenous c-Myc/Max, inhibits TNBC cell proliferation, and sensitizes TNBC cells to the cyclin-dependent kinase inhibitor palbociclib in vitro. In a mouse TNBC model, combination therapy with TEP and palbociclib potently suppresses tumor growth. This study offers a promising nucleic acid-based PROTAC modality for both chemical biology studies and therapeutic interventions of TNBC.