The size dependence of the ferroelectric properties of BaTiO3 nanowires is studied from first principles. We show that the ferroelectric distortion along the wire axis disappears below a critical diameter of about 1.2nm. This disappearance is related to a global contraction of the unit cell resulting from low atomic coordinations at the wire surface. It is shown that a ferroelectric distortion can be recovered under appropriate tensile strain conditions.