Chiral magnetic domain walls are of great interest because lifting the energetic degeneracy of left- and right-handed spin textures in magnetic domain walls enables fast current-driven domain wall propagation. Although two types of magnetic domain walls are known to exist in magnetic thin films, Bloch- and Néel-walls, up to now the stabilization of homochirality was restricted to Néel-type domain walls. Since the driving mechanism of thin-film magnetic chirality, the interfacial Dzyaloshinskii-Moriya interaction, is thought to vanish in Bloch-type walls, homochiral Bloch walls have remained elusive. Here we use real-space imaging of the spin texture in iron/nickel bilayers on tungsten to show that chiral domain walls of mixed Bloch-type and Néel-type can indeed be stabilized by adding uniaxial strain in the presence of interfacial Dzyaloshinskii-Moriya interaction. Our findings introduce Bloch-type chirality as a new spin texture, which may open up new opportunities to design spin-orbitronics devices.