I have a Ring Doorbell 3 on the front and back door of my property. Today we started having the All-new Ring Chime making a sound indicating someone pressed the doorbell button but there is no notification on the Ring App. Checking the app shows no button presses and we can confirm no one at the door or pressed the button. All devices are well powered and well connected to the wifi. No existing doorbell chime is connected or used.
Hey @zelig2. I would recommend resetting the Chime and walking through a new setup in the Ring App just to refresh its connection with the Ring App and your home wifi network. To reset the Chime, you’ll want to hold down the setup button on the side for about 20 seconds. Once that’s done, try setting it up again in the Ring App by following the instructions under Set Up a Device. This process will have you relink the Chime with your Doorbells as well. Let me know how that works for you! 
We just started experiencing the same issue two days ago with an existing Ring doorbell and Ring Chime Pro.
It seems to have started out of nowhere - once the night before last and twice last evening.
I will try to reconnect the Chime Pro to see if this helps and will reply with results (if any).
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