The effect of uniaxial stress on the normal and superconducting states of UPt3 has been investigated for a stress along the hexagonal axis of a single crystal. The coefficient A of the T2 term in the resistivity is found to decrease upon stretching by an amount delta-A/A = -20% for an elongation delta-L/L = +0.25%. This is of opposite sign compared to the effect of hydrostatic pressure, thus revealing a strong anisotropy. The critical temperature T(c) for the onset of superconductivity increases rapidly with elongation, with delta-T(c) = +93 mK for delta-L/L = +0.25%.