Recently observed minute timescale variability of blazar emission at TeV energies has imposed severe constraints on jet models and TeV emission mechanisms. We focus on a robust jet instability to explain this variability. As a consequence of the bulk outflow of the jet plasma, the pressure is likely to be anisotropic, with the parallel pressure $P_{||}$ in the forward jet direction exceeding the perpendicular pressure $P_{perp}$. Under these circumstances, the jet is susceptible to the firehose instability, which can cause disruptions in the large scale jet structure and result in variability of the observed radiation. For a realistic range of parameters, we find that the growth timescale of the firehose instability is $approx$ a few minutes, in good agreement with the observed TeV variability timescales for Mrk 501 (Albert et al. 2007) and PKS 2155-304 (Aharonian et al. 2007).
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