[en] Using the large hadro-produced charm sample collected in experiment E791 at Fermilab, we report the first directly measured constraint on the decay-width difference ΔΓ for the mass eigenstates of the D⁰ -D⁰ system. We obtain our result from lifetime measurements of the decays D⁰→K^-π⁺ and D⁰→K^-K⁺ , under the assumption of CP invariance, which implies that the CP eigenstates and the mass eigenstates are the same. The lifetime of D⁰→K^-K⁺ (the CP-even final state) is τ_KK=0.410±0.011±0.006 ps , and the lifetime of D⁰→K^-π⁺ (an equal mixture of CP-odd and CP-even final states) is τ_Kπ=0.413±0.003±0.004 ps . The decay-width difference is ΔΓ=2(Γ_KK-Γ_Kπ)=0.04±0.14±0.05 ps^-1 . We relate these measurements to measurements of mixing in the neutral D -meson system. copyright 1999 The American Physical Society