  We present a generalization of the so-called Maxwellian extended Bargmann
algebra by considering a non-relativistic limit to a generalized Maxwell
algebra defined in three spacetime dimensions. The non-relativistic
Chern-Simons gravity theory based on this new algebra is also constructed and
discussed. We point out that the extended Bargmann and its Maxwellian
generalization are particular sub-cases of the generalized Maxwellian extended
Bargmann gravity introduced here. The extension of our results using the
semigroup expansion method is also discussed.
