The initiation and propagation of a filament generated by ultrashort laser pulses in turbulent air is investigated experimentally. A filament can be generated and propagated even after the beam has propagated through strongly turbulent regions, with structure parameters C_(n)~(2) as many as 5 orders of magnitude larger than those encountered in the usual atmospheric conditions. Moreover, the filament's position within the beam is not affected by the interaction with a turbulent region. This remarkable stability is allowed by the strong Kerr refractive-index gradients generated within the filament, which exceed the turbulence-induced refractive-index gradients by 2 orders of magnitude.
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