Sources say that this is an age-old Cantonese inspired dish that uses boneless breaded and fried chicken with Chinese vegetables in a thickened sauce.
In a word for word translation, Hon/Hong means "red" while Sue or Siew means "roast". Gai is the Cantonese word for chicken.
It dates back to 100 A.D. according to Food.com. The recipe has rarely been shared in its entirety with anyone in general.
Here's Hong Shu Gai Kew recipe shared by Food.com user, Wadester.
Check out the Top 10 Cantonese Regional Cuisine Recipes, featured at About.com.