The grammar in the sentence is mostly correct, but it could be improved for clarity and readability. A clearer version might be:
"CX started a chat, ended it immediately, and left a DSAT."
However, if "DSAT" is a specific term or acronym that doesn't require an article, the original context of the term will guide whether to include "a" or not. If “DSAT” stands for something that can be counted (like "Dissatisfaction"), adding "a" makes