  In order to extend the recently proposed Monte Carlo Hamiltonian to many-body
systems, we suggest to concept of a stochastic basis. We apply it to the chain
of $N_s=9$ coupled anharmonic oscillators. We compute the spectrum of excited
states in a finite energy window and thermodynamical observables free energy,
average energy, entropy and specific heat in a finite temperature window.
Comparing the results of the Monte Carlo Hamiltonian with standard Lagrangian
lattice calculations, we find good agreement. However, the Monte Carlo
Hamiltonian results show less fluctuations under variation of temperature.
