“Shulchan Aruch (O.H. 675: 3) rules that women are obliged on the mitzva of ner Chanuka, since they were also included in the miracle of its deliverance. Although, Rema (671: 2) writes that the minhag is that all members of the household light their own menorah, Mishna Berura (ibid. 9), excludes women since Ishto kegufo, she constitutes a single entity with her husband. Chasam Sofer (Shabbos 21b) adds that since the mitzva on the onset was to light by the door to the street, our sages instituted that out of a sense of modesty, it was proper the husband should light.
Horav Shlomo Miller’s Shlit’a and other Poskims’ opinion is that when there is no husband, she has to light for herself in her own home, and not by a neighbour. She may however, if she does not desire to make her own brocho, ask a neighbour to recite the brocho in her home. (Being careful to avoid yichud issues ”“ See Kerem Shlomo 31).
Rabbi A. Bartfeld as revised by, Horav Dovid Pam, Horav Aharon Miller, Horav Chanoch Ehrentreu and Horav Kalman Ochs Shlit'a