  Shor's algorithm, which given appropriate hardware can factorise an integer
$N$ in a time polynomial in its binary length $L$, has arguable spurred the
race to build a practical quantum computer. Several different quantum circuits
implementing Shor's algorithm have been designed, but each tacitly assumes that
arbitrary pairs of qubits within the computer can be interacted. While some
quantum computer architectures possess this property, many promising proposals
are best suited to realising a single line of qubits with nearest neighbour
interactions only. In light of this, we present a circuit implementing Shor's
factorisation algorithm designed for such a linear nearest neighbour
architecture. Despite the interaction restrictions, the circuit requires just
$2L+4$ qubits and to first order requires $8L^{4}$ gates arranged in a circuit
of depth $32L^{3}$ -- identical to first order to that possible using an
architecture that can interact arbitrary pairs of qubits.
