The Red Chain is MADE from Azelf, Uxie and Mesprit. Specifically, the red jewels on their tails.
Didn't you guys pay attention to ingame ramblings? ~_~

Also iirc Dialga and Palkia wished them into existence/created them, which explains the connection.
Not to mention...
Blue: Dialga/Saturn/Azelf
Magenta: Palkia/Jupiter/Mesprit
Yellow/Red: Giratina/Mars/Uxie
Dunno why they made Uxie have a yellow head, it fit the theme better with red but still, Giratina has yellow/gold and red.
Draw the connections ~_~

Also I jizz right in my pants every time I hear, or even think about, Jupiter saying "foolishly"... oh my spud that was just an incredible moment of my life uh 8V