She grew up in Atlanta, Georgia and Louisville, Kentucky. Her given name is Zuwena (Swahili for "good"), but "After a while of teachers mispronouncing my name and everyone else in the world, I began introducing myself as ZZ, and it just kind of stuck." Recognized as a talented writer at an early age, her first significant publication was in Seventeen magazine at the age of 19. She is a 1990 graduate of Seneca High School, in Louisville, KY.

Packer attended Yale University, where she received a B.A in 1994. Her graduate work included an M.A. at Johns Hopkins University in 1995 and an M.F.A. from the Iowa Writers' Workshop of the University of Iowa in 1999. She was named a Stegner Fellow in Fiction at Stanford University.

Shortly thereafter, she entered the national literary scene with a high-profile appearance in the Debut Fiction issue of The New Yorker (2000). Her short story in the issue became the title story in her collection Drinking Coffee Elsewhere (Riverhead Books, 2003), which was published to considerable acclaim. As Publishers Weekly put it, "this debut short story collection is getting the highest of accolades from the New York Times, Harper's, the New Yorker and most every other branch of the literary criticism tree." The book was a finalist for the PEN/Faulkner Award, a New York Times Notable Book, and personally selected by John Updike for the Today Show Book Club.

In 2005, she was awarded the prestigious Guggenheim Fellowship for fiction. She is on the faculty of California College of the Arts, where she serves as Senior Visiting Professor of Creative Writing. She is a member of the San Francisco Writers' Grotto, a workspace co-operative that also includes Po Bronson, Julia Scheeres, Tom Barbash, Peter Orner, and Jason Roberts, among others.

She lives in Pacifica, California, a coastal town near San Francisco, but does not consider herself to have a West Coast personality. She believes she primarily adopts more of a serious East Coast mentality in her everyday life and writing.

She is currently at work on a novel set in the aftermath of the Civil War:

The subject is the Buffalo Soldiers who left the South, Louisiana in this case, and traveled to the West...You don't hear much about blacks in the West and I became really fascinated by them. I thought to justify my interest I had better write about them.

She was Writer-in-Residence at the Tulane University English Department Creative Writing Program during the Fall 2007 semester, and was the Lurie Distinguished Visiting Professor of Creative Writing (joining the ranks of Simon Winchester, Ishmael Reed, James D. Houston, Molly Giles, Ursula K. Le Guin, James Kelman, Al Young, Sandra M. Gilbert, and Carolyn Kizer) at San Jose State University during the Spring 2008 semester. In spring 2010, she will be Visiting Professor of Creative Writing in the MFA Program of Creative Writing at Texas State University.

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