  We study non-trivial deformations of the natural imbedding of the Lie algebra
$\fh_1$ of lower triangular matrices (the Heisenberg Lie algebra) into
$gl(3,\mathbb{K})$, where $\mathbb{K}=\mathbb{R}$ or $|mathbb{C}$. Our first
result is the calculation of the first cohomology space
$H^1(\fh_1;gl(3,\mathbb{K}))$. We prove that there are no obstructions for
integrability of infinitesemal deformation and, furthermore, give an explicit
formula for the most general deformation.
