For the last four decades, the predominantly black population of central Brooklyn has been represented in Washington by one of its own, a tradition that dates to the 1968 victory of Shirley Chisholm, the first black woman elected to Congress. But now, in a district whose boundaries were drawn to strengthen black voting power, residents are locked in a wrenching, racially charged debate over a white politician's campaign for Congress. The candidacy of that politician, David Yassky — who has built a reputation as an accomplished, independent-minded councilman — has led to angry accusations of racial carpetbagging. It has also...