  Context: A key science goal of the Gaia-ESO survey (GES) is to use the
kinematics of low-mass stars in young clusters to probe their dynamical
histories and how they populate the field as they become unbound. The
clustering of low-mass stars around the massive W-R binary gamma^2 Velorum was
one of the first GES targets. Aims: To empirically determine the radial
velocity (RV) precision of GES data, construct a kinematically unbiased sample
of cluster members and characterise their dynamical state. Methods: Targets
were selected from colour-magnitude diagrams and intermediate resolution
spectroscopy used to derive RVs and assess membership from the strength of the
Li6708A line. The RV distribution was analysed using a maximum likelihood
technique that accounts for unresolved binaries. Results: The GES RV precision
is about 0.25km/s and sufficient to resolve velocity structure in the low-mass
population around gamma^2 Vel. The structure is well fitted by two kinematic
components with roughly equal numbers of stars; the first has an intrinsic
dispersion of 0.34+/-0.16km/s, consistent with virial equilibrium. The second
has a broader dispersion of 1.60+/-0.37km/s and is offset from the first by
~2km/s. The first population is older by 1-2Myr based on a greater level of Li
depletion seen among its M-stars and is probably more centrally concentrated
around gamma^2 Vel. Conclusions: We consider several formation scenarios,
concluding that the two kinematic components are a bound remnant of the
original, denser cluster that formed gamma^2 Vel, and a dispersed population
from the wider Vela OB2 association, of which gamma^2 Vel is the most massive
member. The apparent youth of gamma^2 Vel compared to the older (>=10Myr)
low-mass population surrounding it suggests a scenario where the massive binary
formed in a clustered environment after the formation of the bulk of the
low-mass stars.[abridged]
