Chiral electric and magnetic structures are observed at domain walls in thin films of the room-temperature multiferroic BiFeO3. Chirality, a foundational concept throughout science, may arise at ferromagnetic domain walls(1) and in related objects such as skyrmions(2). However, chiral textures should also exist in other types of ferroic materials, such as antiferromagnets, for which theory predicts that they should move faster for lower power(3), and ferroelectrics, where they should be extremely small and possess unusual topologies(4,5). Here, we report the concomitant observation of antiferromagnetic and electric chiral textures at domain walls in the room-temperature ferroelectric antiferromagnet BiFeO3. Combining reciprocal and real-space characterization techniques, we reveal the presence of periodic chiral antiferromagnetic objects along the domain walls as well as a priori energetically unfavourable chiral ferroelectric domain walls. We discuss the mechanisms underlying their formation and their relevance for electrically controlled topological oxide electronics and spintronics.