  High-resolution spectroscopy and speckle interferometry reveal the young star
HD 86588 as a quadruple system with a 3-tier hierarchy. The 0.3" resolved
binary A,B with an estimated period around 300 years contains the 8-year pair
Aa,Abc (also potentially resolvable), where Ab,Ac is a double-lined binary with
equal components, for which we compute the spectroscopic orbit. Despite the
short period of 2.4058 day, the orbit of Ab,Ac is eccentric (e=0.086+-0.003).
It has a large inclination, but there are no eclipses; only a 4.4 mmag light
modulation apparently caused by star spots on the components of this binary is
detected with Evryscope. Assuming a moderate extinction of A_V = 0.5 mag and a
parallax of 5.2 mas, we find that the stars are on or close to the main
sequence (age >10 Myr) and their masses are from 1 to 1.3 solar. We measure the
strength of the Lithium line in the visual secondary B which, together with
rotation, suggests that the system is younger than 150 Myr. This object is
located behind the extension of the Chamaeleon I dark cloud (which explains
extinction and interstellar Sodium absorption), but apparently does not belong
to it. We propose a scenario where the inner orbit has recently acquired its
high eccentricity through dynamical interaction with the outer two components;
it is now undergoing rapid tidal circularization on a time scale of ~1 Myr.
Alternatively, the eccentricity could be excited quasi-stationary by the outer
component Aa.
