The Chimu culture was centered on Chimor with the capital city of Chan Chan, a large adobe city in the Moche Valley of present-day Trujillo, Peru. The culture arose about 900. The Inca emperor Topa Inca Yupanqui led a campaign which conquered the Chimu around 1470. This was just fifty years before the arrival of the Spanish in the region.
Expansion
The mature Chimu culture developed in roughly the same territory where the Mochica had existed centuries before. The Chimu was also a coastal culture. It was developed in the Moche Valley north of present-day Lima, northeast of Huarmey, and finishing in central present-day Trujillo. Later, it expanded to Arequipa.  The Chimu appeared in the year 900: Chimor, also known as the Kingdom of Chimor, had its capital "at the great site now called Chanchan, between Trujillo and the sea, and we may assume that Taycanamo founded his kingdom there. His son, Guacri-caur, conquered the lower part of the valley and was succeeded by a son named Nancen-pinco who really laid the foundations of the Kingdom by conquering the head of the valley of Chimor and the neighboring valleys of Sana, Pacasmayo, Chicama, Viru, Chao and Santa."  The estimated founding date of the last Chimu kingdom is in the first half of the 14th century. Nacen-pinco was believed to have ruled around 1370 and was followed by seven rulers whose names are not yet known. Minchancaman followed these rulers, and was ruling around the time of the Inca conquest (between 1462 and 1470). This great expansion is believed to have occurred during the late period of Chimu civilization, called: Late Chimu, but the development of the Chimu territory spanned a number of phases and more than a single generation. Nacen-pinco, "may have pushed the imperial frontiers to Jequetepeque and to Santa, but conquest of the entire region was an agglutinative process initiated by earlier rulers." (17)  The Chimu expanded to include a vast area and many different ethnic groups. At its peak, the Chimu advanced to the limits of the desert coast to the valley of the Jequetepeque River in the north. Pampa Grande in the Lambayeque Valley was also ruled by the Chimu.  To the south, they expanded as far as Carabayallo. Their expansion southward was stopped by the military power of the great valley of Lima. Historians and archeologists contest how far south they managed to expand.

Q: What city did the Chimu expand their territory in?
A: conquering the head of the valley of Chimor and the neighboring valleys of Sana, Pacasmayo, Chicama, Viru, Chao and Santa."

Q: What sort of terrain did the Chimu live on?
A: At its peak, the Chimu advanced to the limits of the desert coast to the valley
Was it difficult for them to find food?
unknown
unknown