It looks like 青椒肉片 (qīng jiāo ròu piàn), pork with green chillies, but without tasting it, or a description of the flavours, I can't be sure.
Are you sure it's chicken? It doesn't look like chicken.
Why do you think the meat isn't fried? It looks fried to me. Most dishes like this are fried.
If it has jalapeño peppers, it's probably American-Chinese. Jalapeño peppers are very rarely found in China.
Three pepper chicken only has two chilli peppers in it. The third is Sichuan peppercorns, which aren't true peppers.
Can you ask somone in the store what it is in English? Or ask them to write it down in Chinese and then show me.
This here is 青椒肉片. Looks similar to your dish but without the onions in this one, although it can.
