Jiā yóu!Oil (yóu, 油) plays a big part in Chinese cooking—even recipes for steamed dishes often call for oil. As I found out traveling around China as a student, different places generally use different oils in their cooking. In my own experience, much of the country uses lard, soy or vegetable oil, while parts of southern China (Guangxi and Guangdong provinces as well as Hong Kong) often use peanut oil. The prevalence of Cantonese cuisine in America, a disproportionate number of Cantonese Americans and simply never needing to ask about ingredients may well account for the assumption of peanut oil's prevalence in China. If you are allergic to peanut oil, always make sure to ask the wait staff, and be persistent. While I've generally found staff to be accommodating, I always follow up until I'm sure they've asked in the kitchen. If your peanut allergy is severe, you may actually want to avoid eating anywhere using an oil you're allergic to unless you can convince them to use separate, clean utensils and woks, as the possibility of cross-contamination is very high.
Additionally, there is the risk of mixed oil. Though the ingredients will be listed on the bottle if bought in a store, oil is often put in a different, unlabeled container and you may not be able to tell. Be aware as well that ingredients used as seasonings, like sesame oil, could be a danger. In some cases, a danger much less well-labeled. An oil that contains chilies may be labeled chili oil but have a peanut oil base, and the chef may not even be aware of this.