Magnetotactic bacteria contain chains of magnetically interacting crystals (magnetosomes), which aid navigation (magnetotaxis). To improve the efficiency of magnetotaxis, magnetosome crystals (which can consist of magnetite or greigite) should be magnetically stable single domain (SD) particles. Larger particles subdivide into non-uniform multi-domain (MD) magnetic structures that produce weaker magnetic signals, while small SD particles become magnetically unstable due to thermal fluctuations and exhibit superparamagnetic (SP) behavior. In this study, we determined the stable SD range as a function of grain elongation and inter-particle separation for chains of identical greigite grains using fundamental parameters recently determined for greigite. Interactions significantly increase the stable SD range. For example, for cube-shaped greigite grains the upper stable SD threshold ze is increased from 107 nm for isolated grains to 204 nm for touching grains arranged in chains. The larger critical SD grain size for greigite means that, compared to magnetite magnetosomes, greigite magnetosomes can produce larger magnetic signals without the need for inter-grain interactions.