Reduced dimensionality offers a crucial information in deciding the type of the quantum ground state in heavy fermion materials. Here we have examined stoichiometric CeCo\(_{2}\)Ga\(_{8}\) compound, which crystallizes in a quasi-one-dimensional crystal structure with Ga-Ce-Co chains along the \(c\)-axis. The low-temperature behavior of magnetic susceptibility (\(\chi\sim-\ln T\)), heat capacity (\(C_p/T\sim-\ln T\)), and resistivity (\(\rho\sim T^{n}\)) firmly confirm the non-Fermi liquid ground state of CeCo\(_{2}\)Ga\(_{8}\). We studied the low-energy spin dynamics of CeCo\(_{2}\)Ga\(_{8}\) compound utilizing zero field (ZF-) and longitudinal field (LF-) muon spin relaxation (\(\mu\)SR) measurements. ZF-\(\mu\)SR measurement reveals the absence of long-range magnetic ordering down to 70 mK, and interestingly below 1 K, the electronic relaxation rate sharply rises, intimating the appearance of low energy quantum spin fluctuations in CeCo\(_{2}\)Ga\(_{8}\).