One of the most influential and articulate modern defenders of egoism

Since you didn't give us a list of choices, there could be more than one answer to this question.  It might depend on what you mean by "modern."  If we're talking anything in the Modern era (from Scientific Revolution forward), then I might go with Friedrich Nietzsche (1844-1900).  Nietzsche essentially founded existentialism (of the atheistic variety) which said we really know nothing else or have nothing else than our own existence to deal with.  So the strong individuals (the "overmen" as he called them) will seize hold of their existence and make something of themselves.

If by "modern" you mean as recent as the 20th century, then I'd pick Ayn Rand (1905-1982), who continued in the tradition of Nietzsche.  She came from the communist Soviet Union to America, and became a powerful proponent of the rights of individuals to live their own lives in their own way.  Famous novels she wrote, such as "The Fountainhead" and "Atlas Shrugged," feature strong individuals who strive to break free from the confines and tedium of the masses.  (That's a theme Nietzsche emphasized also.)