How re-enable design palette in Android Studio

try the Design/Text tabs in the lower left of the layout window

I've just figured this out! If you double click on your .xml file tab at the top it will maximize the designer window. Then on the left you can drag the window to shrink and it will reveal the palette. Then just click on the tab on the left to open the project window.

If you have only the designer and the properties showing and the Properties is on the right, you can get the palette back by switching to a left or right view.

The palette can be shrunk to 0 width. This can be expanded by hovering next to the left edge of the design window, and finding the right-most expand position.