The hot x-ray-emitting plasma in galaxy clusters is predicted to have turbulent motion, which can contribute around 10% of the cluster's central energy density. We report deep Chandra X-ray Observatory observations of the Coma cluster core, showing the presence of quasi-linear high-density arms spanning 150 kiloparsecs, consisting of low-entropy material that was probably stripped from merging subclusters. Two appear to be connected with a subgroup of galaxies at a 650-kiloparsec radius that is merging into the cluster, implying coherence over several hundred million years. Such a long lifetime implies that strong isotropic turbulence and conduction are suppressed in the core, despite the unrelaxed state of the cluster. Magnetic fields are presumably responsible. The structures seen in Coma present insight into the past billion years of subcluster merger activity.