Chu Ko Nu is the best option for the Chinese to counter heavy infantry and light cavalry although they are not a best option against ranged cavalry such as War Wagons, Howdahs, or Yabusame due to their shorter range.
The Chu Ko Nu is relatively cheap, costing only 85 food, and are available since Colonial Age. Due to their fast firing speed, the Chu Ko Nu's arrows deal only 5 damage, less than a Crossbowman, but fires three shots simultaneously and has bigger multipliers; 2.0x against heavy infantry and light cavalry. Also, they can be upgraded to Honored/Guard and Exalted/Imperial levels while the Crossbowmen can't (except for the Portuguese with their Guard-esque Besteiros), which allows them to be used in Fortress Age and beyond. They fall quickly to hand cavalry as they are fairly weak, with only 90 hit points.
The Repelling VolleyHome City Card increase their multipliers against heavy infantry and light cavalry into 3.0x, although they have a multiplier of 0.75x against cavalry, making them particularly weak against heavy cavalry units such as Spahi and Cuirassier.
The Chinese chu ko nu repeating crossbow was known for its simple design and incredible rate of fire. It held a magazine of 10 bolts with steel tips, which it shot in succession, and was operated by grasping the stock in the left hand and working the lever with the right. In that swift movement, a bolt would drop into place, the string would be strung, and then the bolt would be fired, with another bolt dropping in to take its place. The weapon was specifically designed to fire rapidly and be turned on groups of enemy troops at a distance of no more than 150-250 feet. It was especially effective against cavalry. Horses provided large targets for the generally inaccurate chu ko nu, and when the animal was wounded it usually lost control and sowed pandemonium in the surrounding ranks.
Stories of the chu ko nu date back to 250 BCE, when legend has it that the first Chinese emperor Qin Shi Huang used the weapon to shoot sharks for sport. Most accounts, however, have the creation of the chu ko nu occurring during the Chinese Han Dynasty, around the year 200 CE.