Chapter is set in a particular period in time, having four - at the time - in no way related characters, each of them with their own separate story. My best feeling is these stories should be presented in an alternating way, while never directly interfering with each other: short fragment of one (about 3 standard pages or even less than 1 s.p. short) followed by short fragment of another and so on - not necessarily keeping strict order.
I don't really know how to take on on that. Problem is probably deeper than pure formatting, or organization, or composition (to paragraph each passage, to title it or not to, to order them in a certain way etc; although I don't reject any advice on that matter, neither), it's, I imagine, more to the subtleties in the very body of text, which make that kind of narrative convincing, and, having not read anything similar myself, I'd be thankful if you can come up with an example, if you can name a book, recommend a novel which uses, in any part, structure roughly similar to the one I described here, so I can study it myself.
(One character is in 1st person (a child, btw, who is also the narrator, which, when I think of it better, probably makes the schema so problematic, tricky to convincingly shift between characters), others in 3rd person. It's set in the past (two decades before main story line taking place), and is imagined to be more of a character backgrounding, catching the zeitgeist, atmosphere of time and places, less of a real action, which it can't be in all truth, because it would lead nowhere as 4 parts are separate all the way, mixing at no point, except on symbolic level. Also, idea is for it to be the middle chapter of 3 in total. Luckily, though, I haven't written a word yet, so I'm pretty flexible in every respect, and Psicofrenia's answer and Lauren Ipsum's comment have opened some perspectives for me.)