The first giant pandas to have arrived in Mexico were a male called "Pe-Pe" ( 1974-1988) and a female called "Ying-Ying" (1974-1989).
The politics of how these animals arrived in Mexico is quite complicated to explain but it basically came down to a gesture of political / diplomatic gratitude from China because Mexico had been the first North American and Latin American country to establish relations with China.
This was also a period in which China was opening up to the world with a thaw in the coldwar, the Sino-Soviet split and a country that was moving away from an aggressive Maoist stance on the world and seeking warmer diplomatic relations with countries abroad.
Mexico on the other hand was a country that excelled in diplomacy during this period and was notably (and commendably IMO) quick to establish and maintain diplomatic relations even with countries that were maligned by the United States (for example Cuba throughout the cold war).
The first panda birth was in 1980 a female named "Xen-Li " who was notable due to being the first panda born in captivity outside of China but this animal unfortunately died that same year.
However, a year later in 1981 there was another birth of a female called "Tohui" ( 1981-1993 ) who was later to sire "Xin-Xin" with "Chia-Chia" (1972-1991) a male panda that had been sent to Mexico from London.
Here is a vintage news report from 1975 of the first successful birth of a giant panda at Chapultepec, the female "Tohui":
In 1983 another panda was born but this time it was a little male who was christened "Liang-Liang" (1983-1999).
In subsequent years this was followed by another female in 1985 "Xiu-Hua" (1985- 2013) and twins, a male in 1987 "Ping-Ping" (1987-1987) which sadly died as an infant and his sister "Shua-Shua"(1987 to the present) who is now the last surviving Chapultepec Panda.
Here is a shot of signage from the zoo detailing the family tree of the Chapultepec pandas:
Here is a shot of the late "Xin-Hua" in life :
Here is the taxidermy specimen of "Liang-Liang" the only surviving male panda born at Chapultepec which is on display at the nearby Natural History Museum in Mexico City:
The taxidermy specimens of the original founding pair of pandas "Pe-Pe" and "Ying-Ying" are also kept on display to the public at the zoo.
All of the pandas kept by the zoo were / are very significant, symbolic and popular animals with the public and as such they were all very spoilt and exceptionally well cared for and the last survivor "Shua-Shua" continues to be.
Sources: "La diplomacia panda y el caso de México", Carlos Cerda Dueñas, 2007 (Journal: Méx.cuenca pac).
Photo credits to @carlos55.