Building a quantum computer with a one-dimensional (1D) architecture, instead of the typical two-dimensional (2D) layout, could be significantly less difficult experimentally. However such a restricted topology necessitates a large overhead for shuffling qubits and consequently the fault tolerance threshold is far lower than in 2D architectures. Here we identify a middle ground: a 1D segmented chain which is a linear array of segments, each of which is a well-connected zone with all-to-all connectivity. The architecture is relevant to both ion trap and solid-state systems. We establish that fault tolerance can be achieved either by a surface code alone, or via an additional concatenated four-qubit gauge code. We find that the fault tolerance threshold is 0.12%, a feasible error rate with today’s technology, using 15-qubit segments, while larger segments are superior. For 35 or more qubits per segment one can achieve computation on a meaningful scale with today’s state-of-the-art fidelities without the use of the upper concatenation layer, thus minimising the overall device size.