We show that the spectral fluctuations of the Two-Body Random Ensemble (TBRE) exhibit 1/f noise. This result supports a recent conjecture stating that chaotic quantum systems are characterized by 1/f noise in their energy level fluctuations. After suitable individual averaging, we also study the distribution of the exponent alpha in the 1/f^{alpha} noise for the individual members of the ensemble. Almost all the exponents lie inside a narrow interval around alpha=1 suggesting that also individual members exhibit 1/f noise, provided they are individually unfolded
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