  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.
