We found an unusual negative thermal expansion in the simple perovskite MnF3 below the Neel point, where the spins are ordered in an A-type magnetic structure. The structure of MnF3 has been studied between 5 and 500 K using powder neutron and synchrotron diffraction. The structure remains monoclinic C2/c over the entire temperature range. We have found that the interplay of spin and orbital ordering is sufficient to result in a large positive magnetovolume effect without charge ordering. This expansion is reminiscent of the Invar effect observed in certain alloys.