We consider a two-parameter family of cylindrical force-free equilibria, modeled to match numerical simulations of relativistic force-free jets. We study the linear stability of these equilibria, assuming a rigid impenetrable wall at the outer cylindrical radius R_j. We find that equilibria in which the Lorentz factor gamma(R) increases monotonically with increasing radius R are stable. On the other hand, equilibria in which gamma(R) reaches a maximum value at an intermediate radius and then declines to a smaller value gamma_j at R_j are unstable. The most rapidly growing mode is an m=1 kink instability which has a growth rate ~ (0.4 / gamma_j) (c/R_j). The e-folding length of the equivalent convected instability is ~2.5 gamma_j R_j. For a typical jet with an opening angle theta_j ~ few / gamma_j, the mode amplitude grows weakly with increasing distance from the base of the jet, much slower than one might expect from a naive application of the Kruskal-Shafranov stability criterion.
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