Published in Soweto, the owner and editor of the Chronicle were two yo

A and B are wrong: "Published in Soweto" is a description of a magazine
C looks fine
D: 1) the placement of "who would later make his reputation as a political leader" makes it unclear which guy we are talking about;
2) The Chronicle was owned and edited <.…> and publish
E: 1) "being two young journalists" is too wordy
2) wrong structure: "The owner and editor <….> , the Chronicle was published>

There's no dot after "A" in the choice C but that's probably a typo (A William Whitaker)

Official Explanation

Because the phrase "Published in Soweto" modifies the Chronicle, the words "the Chronicle” must appear immediately after the comma next to Soweto for the sentence to be grammatically correct. Choices (A) and (B) violate this rule, so they can be eliminated. There's no clear way to group the remaining answers, so evaluate them individually.

(C) correctly places the modifying phrase "Published in Soweto" directly next to the noun it modifies, "the Chronicle." It doesn't seem to commit any other errors, but check the other choices to be sure.

(D) and (E) both place the information about Soweto at the end of the sentence. In (D), “and publish in Soweto” is left dangling at the end of the sentence, and it seems to refer to A. William Whitaker rather than to the Chronicle. In (E), the phrase “being two young journalists” is passive, and the sentence now seems to say (though because of the awkward construction, its meaning is murky) that the Chronicle was published in Soweto because the owner and editor were two young journalists. Remember that being is hardly ever part of a correct answer on GMAT Sentence Correction!

(D) and (E) are out, and (C) is indeed correct.

TAKEAWAY: To avoid ambiguity, a modifying phrase has to appear as close as possible to what it modifies.