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For λ 0, let πλ be the probability measure on the independent sets of the hypercube {0,1}d in which I is chosen with probability proportional to λ|I|. We study the Glauber dynamics, or single-site-update Markov chain, whose stationary distribution is πλ, and show that for values of λ tending to 0 as d grows, the convergence to stationarity is exponentially slow in the volume of the cube. The proof combines a conductance argument with combinatorial enumeration methods.