Dimensionality plays an essential role in determining the anomalous non-Fermi liquid properties in heavy fermion systems. So far most heavy fermion compounds are quasi-two-dimensional or three-dimensional. Here we report the synthesis and systematic investigations of the single crystals of the quasi-one-dimensional Kondo lattice CeCo$_2$Ga$_8$. Resistivity measurements at ambient pressure reveal the onset of coherence at $T^*approx 20,$K and non-Fermi liquid behavior with linear temperature dependence over a decade in temperature from 2 K to 0.1 K. The specific heat increases logarithmically with lowering temperature between 10 K and 2 K and reaches 800 mJ/mol K$^2$ at 1 K, suggesting that CeCo$_2$Ga$_8$ is a heavy fermion compound in the close vicinity of a quantum critical point. Resistivity measurements under pressure further confirm the non-Fermi liquid behavior in a large temperature-pressure range. The magnetic susceptibility is found to follow the typical behavior for a one-dimensional (1D) spin chain from 300 K down to $T^*$, and first-principles calculations predict flat Fermi surfaces for the itinerant $f$-electron bands. These suggest that CeCo$_2$Ga$_8$ is a rare example of the quasi-1D Kondo lattice, but its non-Fermi liquid behaviors resemble those of the quasi-two-dimensional YbRh$_2$Si$_2$ family. The study of the quasi-one-dimensional CeCo$_2$Ga$_8$ family may therefore help us to understand the role of dimensionality on heavy fermion physics and quantum criticality.
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