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The hypothesis of ``molecular chaos'' is shown to fail when applied tospatially inhomogeneous evolution of a low-density gas, because this hypothesisis incompatible with reduction of interactions of gas particles to``collisions''. The failure of molecular chaos means existence of statisticalcorrelations between colliding and closely spaced particles in configurationspace. If this fact is taken into account, then in the collisionalapproximation (in the kinetic stage of gas evolution) in the limit ofinfinitely small gas parameter the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY)hierarchy of equations yields an autonomous system of kinetic equations for themany-particle distribution functions of closely spaced particles. This systemof equations can produce the Boltzmann equation only in the homogeneous case.It is used to analyze statistical properties of Brownian motion of a test gasparticle. The analysis shows that there exist fluctuations with a 1/f spectrumin the diffusivity and mobility of any particle. The physical cause of thesefluctuations is randomness of distribution of particles' encounters over theimpact parameter values and, consequently, randomness of the rate andefficiency of collisions.  In essence, this is {\bf reprint} of the like author's paper published inRussian in [ Zh. Eksp. Teor. Fiz. {\bf 94} (12), 140-156 (Dec. 1988)] andtranslated into English in [ Sov. Phys. JETP {\bf 67} (12), 469-2477 (Dec.1988)] twenty years ago but seemingly still unknown to those to whom it mightbe very useful. The footnotes contain presently added comments.

BBGKY equations, self-diffusion and 1/f noise in a slightly nonideal gas