Did Christ leave behind a community of believers, or did He institute a Church to teach and sanctify the nations?  If yes, which one?

Since the Protestant Revolution, denomenations and congregations have continued fragmenting in ever increasing numbers.  Each one claims to hold the truth, and yet each one advocates differing interpretations of Christ’s words.  The desire for unity is qualified by a distrust in authority.

And yet, the Catholic Church claims to have an unbroken line of divinely instituted priests and popes, who carry the true message and total meaning of Christ’s words to all peoples in all times.  Could they be right?  Is it the one, true Church of Jesus Christ, the pillar and mainstay of the Truth?