Theoretical investigations are presented, and their results are discussed, of the laser acceleration of a single electron by a chirped pulse. Fields of the pulse are modeled by simple plane-wave oscillations and a cos2 envelope. The dynamics emerge from analytic and numerical solutions to the relativistic Lorentz-Newton equations of motion of the electron in the fields of the pulse. All simulations have been carried out by independent Mathematica and Python codes, with identical results. Configurations of acceleration from a position of rest as well as from injection, axially and sideways, at initial relativistic speeds are studied.