We have searched for evidence of Τ production in 3.5 million hadronic Z decays collected by the L3 detector at LEP in 1991–1995. No signals are observed for the decay chain Z → ΤX; Τ → ℓ⁺ℓ⁻ (ℓ=e,μ), therefore upper limits at 95% confidence level are set on the following Z branching fractions: Br(Z → Τ(1S)X) < 5.5 x 10⁻⁵; Br(Z → Τ(2S)X) < 13.9 x 10⁻⁵; Br(Z → Τ(3S)X) < 9.4 × 10⁻⁵.