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We present measurements of the process pp̅ → WZ + X → ℓ′νℓℓ at √s = 1.96 TeV, where ℓ and ℓ′ are electrons or muons. Using 1 fb-1 of data from the D0 experiment, we observe 13 candidates with an expected background of 4.5 ± 0.6 events and measure a cross section σ(WZ) = 2.7-1.3+1.7 pb. From the number of observed events and the Z boson transverse momentum distribution, we limit the trilinear WWZ gauge couplings to -0.17 ≤ λZ ≤ 0.21(ΔκZ= 0) at the 95% C.L. for a form factor scale Λ = 2 TeV. Further, assuming that Δg1Z = ΔκZ, we find -0.12 ≤ ΔκZ≤0.29 (λZ= 0) at the 95% C.L. These are the most restrictive limits on the WWZ couplings available to date.