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In Act II, Scene 3, which immediately follows the famous balcony scene where Romeo and Juliet pledge their love for each other, Romeo goes to see Friar Lawrence with the express purpose of declaring his love for the "fair daughter of rich Capulet" and asking the friar to perform the marriage between he and Juliet. He hopes that he can convince the friar that he is truly in love with Juliet even though the day before he had been madly in love with another girl named Rosaline. Friar Lawrence quickly rebukes Romeo, condemning his idea of love:

Holy Saint Francis, what a change is here!
Is Rosaline, that thou didst love so dear,
So soon forsaken? Young men’s love then lies
Not truly in their hearts, but in their eyes.
Ultimately, however, the friar agrees to perform the marriage, believing that the pairing of the two youngsters will bring about the end of the feud between their parents. Having secured the aid of Friar Lawrence, Romeo only needs to get a message to Juliet about the time and place of the wedding. He does this in Act II, Scene 4 when the Nurse ventures into the streets where Romeo and the other Montague men are standing around. Her appearance is fodder for the jokes of Mercutio and the Nurse becomes quite angry before privately meeting with Romeo who tells her the plans he has made for Juliet:
Bid her devise
Some means to come to shrift this afternoon,
And there she shall at Friar Lawrence’ cell
Be shrived and married.
"Shrift" is simply the act of confession and Juliet would have certainly been allowed to go the church to meet with Friar Lawrence for that purpose. Romeo also asks the Nurse to wait behind the "abbey wall" to receive a "tackled stair" (rope ladder) which Romeo will use to ascend Juliet's bedroom for their honeymoon. In Act II, Scene 6 the couple is indeed married by Friar Lawrence.