  Bacteria (e.g. E. Coli) are very sensitive to certain chemoattractants (e.g.
asparate) which they themselves produce. This leads to chemical instabilities
in a uniform population. We discuss here the different case of a single
bacterium, following the general scheme of Brenner, Levitov and Budrene. We
show that in one and two dimensions (in a capillary or in a thin film) the
bacterium can become self-trapped in its cloud of attractant. This should occur
if a certain coupling constant $g$ is larger than unity. We then estimate the
reduced diffusion D_eff of the bacterium in the strong coupling limit, and find
D_eff ~ 1/g.
