The response of nanolasers subject to external optical feedback has been analyzed. Calculations have been performed using rate equations, which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. In the analysis, the influence of F and β is evaluated for varying distance from external mirror, current, and feedback rate. It is observed that, in general, increased F and β at low bias currents increases the critical feedback for which chaos occurs as compared to conventional lasers, whereas at higher bias currents, chaos occurs at lower feedback rates. It is also found that for larger F, when increasing the distance from external mirror, the feedback rate at which chaos occurs increases.