The young (~2 Myr) cluster Chamaeleon I is one of the closest laboratories to study the early stages of star cluster dynamics in a low-density environment. We studied its structural and kinematical properties combining parameters from the high-resolution spectroscopic survey Gaia-ESO with data from the literature. Our main result is the evidence of a large discrepancy between the velocity dispersion (sigma = 1.14 \pm 0.35 km s^{-1}) of the stellar population and the dispersion of the pre-stellar cores (~0.3 km s^{-1}) derived from submillimeter observations. The origin of this discrepancy, which has been observed in other young star clusters is not clear. It may be due to either the effect of the magnetic field on the protostars and the filaments, or to the dynamical evolution of stars driven by two-body interactions. Furthermore, the analysis of the kinematic properties of the stellar population put in evidence a significant velocity shift (~1 km s^{-1}) between the two sub-clusters located around the North and South main clouds. This result further supports a scenario, where clusters form from the evolution of multiple substructures rather than from a monolithic collapse. Using three independent spectroscopic indicators (the gravity indicator $\gamma$, the equivalent width of the Li line, and the H_alpha 10% width), we performed a new membership selection. We found six new cluster members located in the outer region of the cluster. Starting from the positions and masses of the cluster members, we derived the level of substructure Q, the surface density \Sigma and the level of mass segregation $\Lambda MSR$ of the cluster. The comparison between these structural properties and the results of N-body simulations suggests that the cluster formed in a low density environment, in virial equilibrium or supervirial, and highly substructured.