Phosphorene, a single sheet of black phosphorus, is an elemental two-dimensional material with unique properties and potential applications in semiconductor technology. While few-layer flakes of the material have been characterized using transmission electron microscopy, very little is known about its response to electron irradiation, which may be particularly important in the context of top-down engineering of phosphorus nanostructures using a focused electron beam. Here, using first-principles simulations, we study the production of defects in a single phosphorene sheet under impacts of energetic electrons. By employing the McKinley-Feshbach formalism and accounting for the thermal motion of atoms, we assess the cross section for atom displacement as a function of electron energy. We further investigate the energetics and dynamics of point defects and the stability of ribbons and edges under an electron beam. Finally, we show that P atomic chains should be surprisingly stable, and their atomic structure is not linear giving rise to the absence of a gap in the electronic spectrum.