When you post a Snapchat story, it is made available immediately to everyone in your Snapchat friends list or who you decide can view your Snapchat story. You can see who is viewing your Snapchat story in real-time and also see how many times someone views your Snapchat story.
At this time, there is no way for Snapchat to notify you when someone opens your Snapchat story. You have to manually check your story’s views (bottom right corner -> my story -> tap story to reveal views).
Even so, if you have a lot of Snapchat friends, it would be nice if you wanted to know if someone in particular viewed your Snapchat story – and not just anyone.
You can control Snapchat’s current notifications in system preferences.