  We derive a semi-analytic criterion for the presence of chaos in compact,
eccentric multiplanet systems. Beyond a minimum semimajor-axis separation,
below which the dynamics are chaotic at all eccentricities, we show that (i)
the onset of chaos is determined by the overlap of two-body mean motion
resonances (MMRs), like it is in two-planet systems; (ii) secular evolution
causes the MMR widths to expand and contract adiabatically, so that the chaotic
boundary is established where MMRs overlap at their greatest width. For closely
spaced two-planet systems, a near-symmetry strongly suppresses this secular
modulation, explaining why the chaotic boundaries for two-planet systems are
qualitatively different from cases with more than two planets. We use these
results to derive an improved angular-momentum-deficit (AMD) stability
criterion, i.e., the critical system AMD below which stability should be
guaranteed. This introduces an additional factor to the expression from Laskar
and Petit (2017) that is exponential in the interplanetary separations, which
corrects the AMD threshold toward lower eccentricities by a factor of several
for tightly packed configurations. We make routines for evaluating the chaotic
boundary available to the community through the open-source SPOCK package.
