Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations, optical conductivity and the validity of Wiedemann-Franz law point to a Fermi liquid regime at low temperature in the underdoped regime. However, the observation of a quadratic temperature dependence in the electrical resistivity down to low temperatures, the hallmark of a Fermi liquid regime, is still missing. Here, we report magnetoresistance measurements in the magnetic-field-induced normal state of underdoped YBa_2Cu_4O_8 which reveal a T^2 resistivity down to 1.5 K. The magnitude of the T^2 term is shown to be consistent with the Fermi surface topology inferred from quantum oscillations and theoretical modelling, and reconciles the Fermi surface reconstruction by charge order with transport properties.