We report nuclear quadrupole resonance (NQR) studies on the chain Cu sites of PrBa2Cu4O8, a quasi-one-dimensional conductor with a nearly quarter-filled band. The nuclear spin-lattice relaxation rate 1/T1 shows a pronounced peak near 100 K caused by fluctuations of electric field gradient (EFG). Similar peak was observed for the spin-echo decay rate 1/T2, however, at a different temperature near 50 K. These results and broadening of the NQR spectrum at low temperatures indicate that slow charge fluctuations of either electronic or ionic origin freeze gradually at low temperatures.There has been increasing interest in quasi-onedimensional (Q1D) correlated electrons. Theoretical studies on generalized Hubbard or t-J models for chains and ladders have revealed rich phase diagram associated with various instabilities towards Mott localization, spin density wave, charge order, and superconductivity [1,2,3] These two compounds show contrasting transport behavior. Pr124 is a highly anisotropic Q1D metal showing extremely large in-plane resistivity anisotropy ρ a /ρ b ∼ 1000 at 4 K [12,13,14], where b is along the chain direction and a is perpendicular to it within the CuO 2 plane. Although ρ b shows monotonic metallic temperature dependence, ρ a exhibits a broad peak near 130 K, indicating incoherent transport perpendicular to the chains at high temperatures. The angle resolved photoemission spectra (ARPES) [15] also revealed a clear one-dimensional dispersion which crosses the Fermi level near the momentum k b ≃ π/4, pointing to a nearly quarter-filled conduction band. In Pr123, the spectral weight of the chain contribution to the optical conductivity [9] as well as the ARPES spectra [16] are also consistent with an approximately quarter-filled conduction band. However, semiconducting behavior of the dc-resistivity, steep suppression of the optical conductivity below 0.1 eV and vanishing ARPES intensity near the Fermi level all indicate the existence of a charge gap. Nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) experiments in Pr123 [17] revealed line broadening and anomalies in relaxation rates, which were ascribed to a charge ordering instability.Apparent absence of static charge order in Pr124 may be due to slight deviation from the quarter-filling [15] or to the geometrical frustration of intersite Coulomb interactions in zigzag chains [18]. However, dynamic signature towards charge order instability is indicated by the optical conductivity in Pr124, which splits into a zero-energy Drude part with a small weight and a finite energy mode centered at 40 meV [10]. In this letter, we report results of NQR experiments for the chain Cu sites in Pr124. We found a pronounced peak in the temperature dependences of the nuclear spin-lattice relaxation rate (1/T 1 ) and spin-echo decay rate (1/T 2 ), as well as broadening of the NQR spectra, indicating gradual freezing of fluctuations of electric field gradient (EFG) with decreasing temperature.The powder sample of Pr124 was synthesized by solid stat...