1. Create a Snapchat Story and tap the blue arrow in bottom right.
2. Tap + Custom in the top right.
3. Select Private Story and select your Snapchat friends you want to share the story with.
4. Tap the checkbox in bottom right corner.
5. Finally, you can customize your Snapchat story with options including naming the story and auto-save to memories. Tap Create Story.
Note: You will be forced to name your story if you do not at this screen.
Your private Snapchat Story will appear under Stories in it's own section.