  Recent numerical results showed that thermalization of Fourier modes is
achieved in short time-scales in the Toda model, despite its integrability and
the absence of chaos. Here we provide numerical evidence that the scenario
according to which chaos is irrelevant for thermalization is realized even in
the simplest of all classical integrable system: the harmonic chain. We study
relaxation from an atypical condition given with respect to "random" modes,
showing that a thermal state with equilibrium properties is attained in short
times. Such a result is independent from the orthonormal base used to represent
the chain state, provided it is random.
