The theme of the third group is the native Indians of Cuba, the Tainos, that built a society in that the agriculture was a fundamental economic activity and the pottery a distinctive feature, as well as carving and decoration of wood, bone, shell and rock. Tainos settled in Cuba about five centuries before the arrival of Christopher Columbus in 1492. They are distinguished from the other aboriginal Cuban societies in the typical occipitofrontal deformation of their skulls.

In this section of the museum, there are many valuable pieces from the perspective of anthropology, like Idolo del Tabaco, Idolo de Bayamo, Dujo de Santa Fe and Yucahú Bagua Maórocote.

Undoubtedly, one of the most valuable pieces of the collection of the museum is the idol or cemí associated with tobacco, Idolo del Tabaco (or Cemí de Gran Tierra). Cemí is god or supernatural entity that has certain social powers to protect the community or the individual in the Taino society. Idolo del Tabaco that is considered the main piece of the Cuban aboriginal archeology, is an elongated, spindle-shaped idol, carved from guayacán negro (a small tree, native to the southeast of the island, that has incredibly hard wood, used by native Indians in making of tools). It is about one meter high (92 cm). It had several inlaid of seashells; however, only the left eye still has the seashell inlaid, whereas the others were dropped off the statue. As it is known that the settlers of the Antilles in the pre-Columbian time were using the seashells in carving the wood, thus, it is estimated that Idolo del Tabaco was shaped in the same way.

It was found by two peasants on the Plateau de la Gran Tierra, located in Maisí, the province of Guantánamo, in 1903. Even though it was called as Idol of Tobacco for the first time by the anthropologist Mark Raymon Harrington in 1921, no trace of tobacco was detected in the biochemical study, carried out on the interior of the idol. However, different hallucinogenic substances and fatty acids from roots and seeds were detected in this study that led to the idea that this relic, embodying the image of one of the Taino’s gods, was in fact a ceremonial mortar, used to pulverize tobacco leaves and to prepare the compound, used in cohoba. Cohoba is an old Taíno ceremony in which the ground seeds of the cojóbana tree were inhaled in a twin-nasal, Y-shaped pipe. Despite all, it continues to call the wooden statue as Idolo del Tabaco today, even though the only argument that warrants such a denomination, is its spindle shape, similar to that what we know as cigar today.

The same figure was also found in some engravings on stone. The most spectacular one is figure that was discovered by the archeologist Mark Harrington inside of the cave of La Patana in Maisí in 1915, along with six other engravings of animal figures. That Idolo del Tabaco was carved into a tall stalagmite of more than one meter. Harrington cut the stalagmite into three pieces by a saw and took it to the US. Currently, it is on the exhibition in the Museum of the American Indian in New York. 

Since 1997 the Cemí de Gran Tierra is the symbol of the province of Guantánamo, and every year the replicas of the idol in small format are given to personalities that had great contribution in the development of the eastern territory (like Fidel and Raúl Castro, cosmonaut Arnaldo Tamayo Méndez and boxer Félix Savón).