Literally, ‘吃鸡’ means ‘eat chicken’.
However, it has recently extended its meaning as an online buzzword — referring the popular game 绝地求生：大逃杀 or PlayerUnknown’s BattleGrounds (PUBG).
‘吃鸡’ is the abbreviation of ‘大吉大利，晚上吃鸡’ which means ‘Winner, winner, chicken for dinner’.
The slogan actually means to say that you have been blessed by fortune, congratulations! So lets have chicken for dinner tonight!
This is with the historical background that in ancient China, meat was scarce and limited to those who were rich enough to afford it. Therefore, any celebrations would usually be accompanied by the rare presence of meat, usually chicken meat!
It is a slogan of the system when you win the game in PUBG. It is so interesting that now people don’t say the full name of the game anymore and just use ‘吃鸡’ instead.