  We prove that for an arbitrary $\varepsilon > 0$ holds \[ \chi (\mathbb{R}^3
\times [0,\varepsilon]^6) \geq 10, \] where $\chi(M)$ stands for the chromatic
number of an (infinite) graph with the vertex set $M$ and the edge set consists
of pairs of monochromatic points at the distance 1 apart.
