How do you rescue chai on magical starsign

Use wind magic to blow the Inacessable Treasure Chest off of it's cliff, then talk to the fisherman near Honey Mint to obtain the Tempus Forget. Afterwards, return to the Space police HQ and use the Tempus Forget when prompted. Just as Twigadamus showed.

Chai is in the shaking box near the top of the building. However, do note that after recruiting him you will never be able to enter Space Police HQ again, so take a good look around the building first.