John L. Sorenson discusses the use of litters and the wheel in Mesoamerica; suggests the litter was the "chariot" in the Book of Mormon.
John L. Sorenson, Images of Ancient America: Visualizing Book of Mormon Life (Provo, UT: Foundation for Ancient Research and Mormon Studies, 1998), 58-59
The Litter
Cultural preference throughout Mesoamerica called for a person of social prestige to be transported by litter. The system was sensible enough in practical terms—in whatever remote spot a group of travelers might stop, fresh carriers could be found so long as carriage depended on human muscles. Furthermore, prestige entered in; this form of transport was reserved for nobility and others of the upper social levels. To have used any other mode would have been to give up privilege and demean oneself. Privileged and sacred leaders were similarly carried in the stretch of the Old World from the eastern Mediterranean through South-east Asia in earlier times.
The Wheel
It was once supposed that ancient American peoples did not even know the principle of the wheel, but discoveries by archaeologist of many small wheeled “toys” has changed that view. The “toys” are now understood to have been miniature ceremonial objects connected with ideas about death, burial, and, probably, the sun. Mexican specimens date from as early as the first century A.D. In the Near East similar wheeled models were in use from before 3000 B.C. into medieval times, having spread as far as western Europe and China.
The usual interpretation of these objects by Mesoamericanist scholars is that while the prehistoric peoples obviously knew the principle of the wheel, for unknown reasons they never translated the idea into practical vehicles. Yet these some scholars celebrate the inventive capabilities of the early Americans. Would they have been familiar with these miniatures for at least fifteen hundred years without trying to make a practical vehicle? In fact, the vehicle concept was known. When the Spaniards invaded Guatemala, they reported that the Quiché Indians used “military machines” consisting of wooden platforms mounted on “little rollers” to haul weapons around one battlefield to resupply their soldiers. But on the broken terrain so common throughout Mesoamerica, wheeled vehicles may rarely have seemed worth the trouble. (One interesting suggestion is that Mesoamericans lacked lubricants that would have made full-sized wheels practical.)
Archaeologists have not found direct evidence of any useful wheeled vehicle. This lack in Mesoamerica is made less surprising when we learn that no fragment of a chariot has ever been uncovered in the Holy Land, despite the fact that thousands of them are reported by the Bible to have been used.
Visualizing Book of Mormon Life
In two situations reported in the Book of Mormon, a word is used that might be supposed to refer to wheeled vehicles, once among the Lamanites and once among the Nephites. Yet what is said is so brief that we are left unclear about the nature of their “chariots.”
In the story of Ammon in the land of King Lamoni, “horses and chariots” were made ready to “conduct” the king to the land of Middoni (Alma 18:9; see 18:10, 12; 20:6). Because nothing is said or hinted about mounting, riding, or dismounting from a vehicle, we cannot confidently conclude that vehicles were used to carry people, although this may have happened. Later, according to 3 Nephi 3:22, the Nephites who gathered at a refuge zone where robbers would besiege them had “taken their horses, and their chariots.” Yet in 3 Nephi 4:4, the “horse” are considered along with “cattle” as “provisions.” So it remains a mystery what “chariot” means in these texts. The word might have been used in a nonliteral sense. Nonliteral language abounds in the record. For instance, the Savior speaking to the Nephites applied the words of Isaiah to a future day when Israel was to be gathered, prophesying, “I will destroy thy chariots” (3 Nephi 21:14) as well as modern “graven images” (3 Nephi 21:17) and “groves” (3 Nephi 21:18), whatever they might be. Clearly some analogy, not literality, was intended in these cases.
The text of the Bible also leaves the word ambiguous. Hebrew roots translated to English as “chariot” include the dictionary meaning of “wagon or chariot” but also “litter, portable couch” or human-borne “sedan” chair (in the Talmud the same expression even meant nuptial bed).
“Chariots” aside, nothing else in the Book of Mormon indicates that the people it describes used vehicles.