Amyloid fibrils derived from antibody light chains are key pathogenic agents in systemic AL amyloidosis. They can be deposited in multiple organs but cardiac amyloid is the major risk factor of mortality. Here we report the structure of a λ1 AL amyloid fibril from an explanted human heart at a resolution of 3.3 Å which we determined using cryo-electron microscopy. The fibril core consists of a 91-residue segment presenting an all-beta fold with ten mutagenic changes compared to the germ line. The conformation differs substantially from natively folded light chains: a rotational switch around the intramolecular disulphide bond being the crucial structural rearrangement underlying fibril formation. Our structure provides insight into the mechanism of protein misfolding and the role of patient-specific mutations in pathogenicity.