Definition
To chase after the promise of a continually fulfilling high from an addictive substance.
Origins
Calque of Cantonese 追龍 /追龙 (zeoi¹ lung⁴), a slang phrase of Cantonese origin from Hong Kong. Chasing refers to the careful movement of the liquid in order to keep it from coalescing into a single, unmanageable mass.
How People Actually Use It
(1) "Chasing the dragon" is a method of smoking opium (opium is often referred to as a dragon in asian cultures). The opium is heated on some kind of metal and a fine line of smoke evolves from the heated drug. This smoke is now to be "chased" (meaning breathed in), often through a small tube, like a straw. (2) Also used to describe a similar method of smoking other drugs (heroine, crack, etc)
"In many cultures it is common to chase the dragon every day."
Source: Urban Dictionary