“Hi,” she says, striding into the room with a smooth gait and a low, sure voice. “I’m Chelsea!” The handshake is confident, the eyes firmly fixed. With the ease of her father and the directness of her mother, Chelsea Clinton is stepping out into the world. At 33, she wears her political royalty in triplicate: There are her famous parents, of course, but also her mother-in-law, former Pennsylvania congresswoman Marjorie Margolies. After several years in the private sector (with McKinsey & Company, then with a hedge fund), Clinton has emerged onto the civic stage in her own right, graceful and...