The Middle English women writers best known today are the religious writers Julian of Norwich and Margery Kemp. The works of both are printed, in modern English, in the Anthology of Middle English Literature created by Anninna Jokinen:  

Julian of Norwich, Revelations of Divine Love. For further information see umilta, the Julian of Norwich websites compiled by Julia Bolton Holloway.

Margery Kemp, The Book of Margery Kemp. See also Mapping Margery Kemp, a most useful site made by Virginia Raguin and Sarah Stanbury at Holy Cross.

The best woman writer in Middle English is the anonymous author of The Flower and the Leaf and (possibly) the Assembly of Ladies (which may be by a second woman). Both works were long thought to have been Chaucer's own productions, and John Dryden so admired the Flower and the Leaf he translated it into modern English. See:

The Flower and the Leaf (Original)
The Flower and the Leaf (Trans. John Dryden)
The Assembly of Ladies

The most important woman writer of Chaucer's time was Christine de Pisan (ca. 1364- aft. 1429). Chaucer may not have known of her, though his younger admirer, Thomas Hoccleve, freely translated her "Epistle of Cupid" into Middle English. Her best known work is The Book of the City of Ladies. The illustration shown below is from a manuscript of that work.

See also The Writings of Christine de Pisan, sel. and ed. Charity C. Willard, New York, 1994 [PQ1575.A27 1994].  

Chaucer may have known the works of Marie de France; her fable of the Cock and the Fox is a possible source of the Nun's Priest's Tale, and he could have known her Breton lays. She is one of the most charming writers of the Middle Ages. See the homepage of the International Marie de France Society, which has much good information and useful links, including an annotated verse translation of Lais of Marie de France by Judith P. Shoaf. In addition to the delicate lays, Marie also wrote a lively collection of fables, two of which are fabliaux -- tales of a woman and her paramour. For a translation of the whole collection see

Marie de France, Fables, ed. and tr. Harriet Spiegel, Univ. of Toronto Press, 1987 [PQ 1494.F3 E5 1987]

For some insight into the literacy of women (of the country gentry class) in the fifteenth century, see The Paston Letters.

For a bibliography see:

Bibliography of Works by and about Women Writers of the Middle Ages compiled by Judith Sloger for The Camelot Project of The Robbins Library at the University of Rochester.

A page on "Distinguished Women Past and Present," created by Danuta Bois, provides thumbnail sketches of a number of important women of the Middle Ages, and it also has a useful list of related sites.

Go to the questia site for an impressive number of books and articles on women in the Middle Ages (and any other aspect of historical and literary study).

For a good discussion of the general state of female literacy in England at the time see

Rebecca Krug, Reading Families: Women's Literate Practice in Late Medieval England, Cornell University Press, 2002. [PR275.W6 K78 2002]