The Necessary Feather is the 3rd chapter in Tsubasa: Reservoir Chronicle.
Yuuko explains that the journey to the next worlds will be difficult; that people they have known previously may exist in other worlds, living different lives, and that there will be worlds where one cannot follow reason and common sense. She warns Syaoran that she herself isn't even sure when or where Sakura's memories are, much less if he could collect them all. Nonetheless, he maintains his resolve, and they leave her world and their journey begins.
Syaoran's first thoughts when he awakens in the new world is Sakura, whose body feels as cold as ice. His new companions introduce themselves, and Fai D. Flowright suddenly discovers one of Sakura's "feathers" in Syaoran's cloak. As the feather enters Sakura's body, she warms up. As they all wonder how to find the other feathers, Mokona excitedly explains that he can sense wherever a feather is located (ie. he goes "Mekyo!").
Kurogane speaks up, saying that he doesn't want to search for the feathers, and that Syaoran is selfish to think that they will all just help him. Syaoran replies that he doesn't want to be an annoyance to them, but Fai interrupts him to say that no matter what their individual wishes may be, that saving Sakura should be their top priority.
The door opens, and Sorata and Arashi enter. They know that Yuuko, the witch of dimensions, has sent them to their world and they couldn't have come to a better place. They have arrived at the Republic of Hanshin.