Sit down to eat - similar in meaning to the British term 'tuck in'.
A chow is a breed of Chinese dog. The reputation that poor Chinese had for eating dogs has led to chow being thought of as a slang term for food. In fact, the use of 'chow' to mean food predates the naming of the chow breed of dog. Nevertheless, that reputation for eating animals which are regarded in western countries only as pets also resulted in the Australian slang term for Chinese food - 'chow miaow' (recorded since at least 1948).
'Chow', in the sense of food, is recorded from the mid-19th century. In Spirit of Age, 1856 we get this line:
"Ah Chow- ah in the Celestial lingo means Mr, Chow something good to eat."
In Sir Henry Yule and Arthur Burnell's Hobson-Jobson: being a glossary of Anglo-Indian colloquial words and phrases, 1886 were unambiguous in their definition:
"Chow is in 'pigeon' applied to food of any kind."
The phrase 'chow down' originated in the U.S. military around WWII. The earliest printed citation I can find is from The Hammond Times, December 1942, in a story about life on a submarine:
"'Chow down, sir' a Negro mess attendant in a white coat informed.... "Served on navy blue and white china we put away steak, potatoes, peas and ice cream."