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The investigation [Gupta etal, Appl. Phys. Lett. 91, 211101 (2007)] for electron acceleration by a tightly focused laser beam is revisited by including the effect of laser frequency chirping. The frequency chirping plays an important role to enhance the electron energy if the laser is tightly focused. Due to the combined effect of frequency chirping and tight focusing of a laser beam, an electron can be accelerated for a longer time in vacuum. As a result, from the proposed investigation, the electron energy gain during the laser acceleration is found to be considerably higher.