  An analytical expression for the maximal Lyapunov exponent $\lambda_1$ in
generalized Fermi-Pasta-Ulam oscillator chains is obtained. The derivation is
based on the calculation of modulational instability growth rates for some
unstable periodic orbits. The result is compared with numerical simulations and
the agreement is good over a wide range of energy densities $\epsilon$. At very
high energy density the power law scaling of $\lambda_1$ with $\epsilon$ can be
also obtained by simple dimensional arguments, assuming that the system is
ruled by a single time scale. Finally, we argue that for repulsive and hard
core potentials in one dimension $\lambda_1 \sim \sqrt{\epsilon}$ at large
$\epsilon$.
