Breast and other estrogen receptor α-positive cancers tend to develop resistance to existing drugs. Chalcone derivatives possess anticancer activity based on their ability to form covalent bonds with targets acting as Michael acceptors. This study aimed to evaluate the anticancer properties of a series of chalcones (7a–l) with a sulfonamide group attached to the vinyl ketone moiety. Chalconesulfonamides showed a potent antiproliferative effect at low micromolar concentrations against several cancer cell lines, including ERα-positive 4-hydroxytamoxifen-resistant MCF7/HT2. Immunoblotting of samples treated with the lead compound 7e revealed its potent antiestrogenic activity (ERα/GREB1 axis) and induction of PARP cleavage (an apoptosis marker) in breast cancer cells. The obtained compounds represent a promising basis for further development of targeted drugs blocking hormone pathways in cancer cells.