From Art Institute of Chicago:
This canvas is Edgar Degas's most ambitious statement on the theme of the millinery shop. Although the young woman is presumably a hatmaker examining her handiwork—with her lips pursed, perhaps around a pin—it has also been suggested that she could be a client about to try on a hat, since she wears an expensive fur-trimmed dress and kid gloves. X-ray examination revealed that this figure originally represented a customer, but in his rethinking of the subject, Degas withheld the information necessary to determine her identity.
— Permanent collection label