We investigate cosmological scenarios of generalized Chaplygin gas in a universe governed by Horava-Lifshitz gravity. We consider both the detailed and non-detailed balance versions of the gravitational background, and we include the baryonic matter and radiation sectors. We use observational data from Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB), along with requirements of Big Bang Nucleosynthesis (BBN), to constrain the parameters of the model, and we provide the corresponding likelihood contours. We deduce that the present scenario is compatible with observations. Additionally, examining the evolution of the total equation-of-state parameter, we find in a unified way the succession of the radiation, matter, and dark energy epochs, consistently with the thermal history of the universe.

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