You do have to get the Staff first, then the Chain.
There is also another post-game chest in the upper section below the Holy Door, which requires the Water Ring.

NOTE: You do not need to trudge back to the Post-Game Holy Door a the top of the map right after beating the game. This only contains a couple of meteorites if I remember correctly. So dont struggle back up there if you dont need to. Unless you happen to be there for the XP or coming back with water ring.

To view this map in detail, click the image below, then click the link at the top of the pop-up. You can then expand the image and even zoom in.

• Red indicators are same-map teleports. These are 'white' portals that appear on the islands.
  
• Yellow Indicators are map-to-map doors, or area portals.
  
• White are post-game contents.
  
  
• The Yellow X's indicate area portals, but be weary; the teleport is for the lower level of the serpent room.

From the Start section, head to the east side and up the stairs. Stand on the pendulum to activate it and ride it to the west side of this map.

Hop map areas to the far west map, to another 'stopped time' section. Here, at the south end, stand on the pendulum and ride it to the north. Exit to the next North map area.

In this map section with the Staff, examine the staff, examine the mirror and examine the staff again.
Next, head for the Chain area.

There are a couple ways to get there, though the Chain map segment has One-Way stairs, so I do recommend heading back south from the Staff map area, east to the next map area and north to the second island area. From here hopping to the far east side of the map to get to the top of the Chain area. As soon as you approach it, it will unlock the third pendulum.