China has literally hundreds of commercially produced hot sauces in addition to those made in-house in restaurants or at home.
One of the best known is S: 桂林辣椒酱; T: 桂林辣椒醬 (guì lín là jiāo jiàng) Guilin Chilli Sauce. Its popularity, I suspect, is more to do with Guilin being one of China's top tourist destinations than to do with any inherent superiority in the product.
It's an OK hot sauce but there are better. See the hot sauce topic here for hot sauces around the world, including China.
Beware: Guilin's popularity has lead to a number of copycat products such as this.
Note that it says 桂林风味辣椒酱. That extra 风味 (fēng wèi) dropped casually into the name means 'distinctive flavour or distinctive style', and is only included for legal reasons. The sauce is made in Zhongshan, a city in Guangdong province, far from Guilin. Despite being a knock off, it is more expensive than the real thing.
Caveat emptor, as Chairman Mao said.
I'm told Guilin 'style' sauce is available in the US from Amazon. The real stuff may be available in Asian markets.
