High-resolution spectroscopy and speckle interferometry reveal the young star HD 86588 as a quadruple system with a 3-tier hierarchy . The 0 \farcs 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 \pm 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 \sim 1 Myr . Alternatively , the eccentricity could be excited quasi-stationary by the outer component Aa .