There have been some proposals that stem cells exist in the ovarian surface epithelium (OSE) of the adult human ovary; however, no direct evidence of such cells has been given until now. The aim of this study was to isolate the putative ovarian stem cells (OSCs) from the OSE layer in women with no naturally present oocytes and follicles—20 postmenopausal women and five women with premature ovarian failure. Small round cells with a bubble-like structure and diameters from 2 to 4 μm were isolated from the material obtained by OSE scraping. They expressed early embryonic developmental markers such as stage-specific embryonic antigen-4 and Oct-4, Nanog, Sox-2, and c-kit transcription markers, and they displayed prominent c-kit immunohistochemical staining. These cells were separated by density gradient centrifugation and grown in vitro, where they proliferated. Some of them grew intensively and reached a diameter of approximately 20 μm after 5–7 days. In the OSE cell culture, oocyte-like cells developed, which reached a diameter of up to 95 μm and expressed Oct-4A, Oct-4B, c-kit, VASA, and ZP2 transcription markers, corresponding to early oocytes. They did not express SCP3 meiotic marker. In conclusion, the discovered cells are proposed to represent the adult OSCs with the expression of embryonic stem cell markers. The expression of germ lineage marker c-kit points toward their primordial germ cell ancestry. A new term “embryonic-like stem cells of the adult” is proposed for embryonic-like stem cells that might persist in various tissues and organs of adults. These findings could be used for further studies aimed at the autologous treatment of ovarian infertility and degenerative diseases.