  This paper is devoted to constructing approximate solutions for the classical
Keller--Segel model governing \emph{chemotaxis}. It consists of a system of
nonlinear parabolic equations, where the unknowns are the average density of
cells (or organisms), which is a conserved variable, and the average density of
chemoattractant.
  The numerical proposal is made up of a crude finite element method together
with a mass lumping technique and a semi-implicit Euler time integration. The
resulting scheme turns out to be linear and decouples the computation of
variables. The approximate solutions keep lower bounds -- positivity for the
cell density and nonnegativity for the chemoattractant density --, are bounded
in the $L^1(\Omega)$-norm, satisfy a discrete energy law, and have \emph{ a
priori} energy estimates. The latter is achieved by means of a discrete
Moser--Trudinger inequality. As far as we know, our numerical method is the
first one that can be encountered in the literature dealing with all of the
previously mentioned properties at the same time. Furthermore, some numerical
examples are carried out to support and complement the theoretical results.
