We study the entanglement properties of a molecular three-qubit system described by the Heisenberg spin Hamiltonian with anisotropic exchange interactions and including an external magnetic field. The system exhibits first-order quantum phase transitions by tuning two parameters, x and y, of the Hamiltonian to specific values. The three-qubit chain is open-ended so that there are two types of pairwise entanglement: nearest-neighbour (nn) and next-nearest-neighbour (nnn). We calculate the ground and thermal state concurrences, quantifying pairwise entanglement, as a function of the parameters x, y and the temperature T. The entanglement threshold and gap temperatures are also determined as a function of the anisotropy parameter x. The results obtained are of relevance in understanding the entanglement features of the recently engineered molecular Cr7Ni-Cu2+-Cr7Ni complex which serves as a three-qubit system at sufficiently low temperatures. © 2009 IOP Publishing Ltd.