The Chihuahuan Desert defined in attributes
Geography:
+ SW North America between the higher mountains; most is in Mexico
+ physiography is related and connected to the Mexican Plateau
+ high elevation (mostly over 2000 ft), except the extreme eastern sections (Langtry TX is 1289 ft)
+ highest elevational limits are desert grassland and Madrean vegetation
Some place names:
+ cities: El Paso, Las Cruces, Albuquerque
+ towns: Carrizozo, Fort Sumner, Roswell, Alamogordo, Carlsbad, Wilcox, Marfa, Fort Stockton, Presidio, Terlingua, Langtry
Climate:
+ arid (precipitation less than 50% of evaporation), with a summer wet season and a winter-spring dry season
+ mean tempearature of coldest month = above 32F
+ summers are hot = often above 90F in the daytime
+ growing season = over 175 days
+ desert willow, screwbean, ocotillo, whitethorn, torrey yucca, soaptree yucca
+ creosote, tarbush, broom dalea, mariola, plume tiquilia, allthorn, littleleaf sumac
+ lechuguilla, blue barrel, black-spined prickly pear, engelmann prickly pear
+ black grama, desert marigold, bush muhley, desert bahia, tobosa
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(there are more plants, but those came to mind first / some are native in adjacent SW dryland areas, too)
The Chihuahuan Desert defined in maps (click on image to enlarge)
Chihuahuan Desert Map DRAFT (http://www.xericzone.com/), David Cristiani

"New Mexico in Maps", Jerry O. Williams (this is probably the best, most detailed map for the Rio Grande valley portions of the CD)

"Landscaping with Native Plants of the Southwest", George O. Miller (probably the most accurate map of the CD in a book, let alone one on horticulture...and a great book, too)

Unknown website, sent by George O. Miller to me (I think he mentioned referring to this for the above book map he did, but he nor I can find it online...one of the most accurate for the CD in New Mexico)
"Biotic Communities of the Southwest", U of A (this map from UTEP geographer Robert Schmidt is that book's most accurate one to portray the Chihuahuan Desert in NM...their own detailed map lacks for the CD, even though it is very attractive graphically...)

"Desert Landscape Architecure", John C. Kreig

Carlsbad Caverns National Park

"New Mexico Range Plants", New Mexico State University

Sevilleta National Wildlife Refuge

Smokey Bear State Park (Capitan NM)

Living Desert State Park (Carlsbad NM)

A final note: the Chihuahuan Desert is one of the least studied desert regions in the world, though it is the 2nd largest or possibly the largest desert ecoregion in North America. There are several organizations and websites covering the Chihuahuan Desert in some form, though few accurate maps or thorough species checklists have been compiled for the Chihuahuan Desert ecoregion.
I think this is due to not understanding the associations of vegetation and its relationship to climate, a huge weakness in many maps, and certainly many people in horticulture.
So there you have it!