Who was Melchizedek? Melchizedek ("King of Justice" in Hebrew) is mentioned in Genesis 14 as receiving the dime from Abraham, and breaking bread with him:


  18 And Melchizedek king of Salem brought forth bread and wine: and he
  was the priest of the most high God.
  
  19 And he blessed him, and said, Blessed be Abram of the most high
  God, possessor of heaven and earth:
  
  20 And blessed be the most high God, which hath delivered thine
  enemies into thy hand. And he gave him tithes of all.


Psalm 110:4 depicts Jesus as a priest after the order of Melchizedek:


  4 The LORD hath sworn, and will not repent, Thou art a priest for ever after the order of Melchizedek.


Paul mentions Melchizedek in Hebrews 7 and associates Jesus to him again:


  1 For this Melchisedec, king of Salem, priest of the most high God,
  who met Abraham returning from the slaughter of the kings, and blessed
  him;
  
  2 To whom also Abraham gave a tenth part of all; first being by
  interpretation King of righteousness, and after that also King of
  Salem, which is, King of peace;
  
  3 Without father, without mother, without descent, having neither
  beginning of days, nor end of life; but made like unto the Son of God;
  abideth a priest continually.
  
  4 Now consider how great this man was, unto whom even the patriarch
  Abraham gave the tenth of the spoils.
  
  5 And verily they that are of the sons of Levi, who receive the office
  of the priesthood, have a commandment to take tithes of the people
  according to the law, that is, of their brethren, though they come out
  of the loins of Abraham:
  
  6 But he whose descent is not counted from them received tithes of
  Abraham, and blessed him that had the promises.
  
  7 And without all contradiction the less is blessed of the better.
  
  8 And here men that die receive tithes; but there he receiveth them,
  of whom it is witnessed that he liveth.
  
  9 And as I may so say, Levi also, who receiveth tithes, payed tithes
  in Abraham.
  
  10 For he was yet in the loins of his father, when Melchisedec met
  him.
  
  11 If therefore perfection were by the Levitical priesthood, (for
  under it the people received the law,) what further need was there
  that another priest should rise after the order of Melchisedec, and
  not be called after the order of Aaron?
  
  12 For the priesthood being changed, there is made of necessity a
  change also of the law.
  
  13 For he of whom these things are spoken pertaineth to another tribe,
  of which no man gave attendance at the altar.
  
  14 For it is evident that our Lord sprang out of Juda; of which tribe
  Moses spake nothing concerning priesthood.
  
  15 And it is yet far more evident: for that after the similitude of
  Melchisedec there ariseth another priest,
  
  16 Who is made, not after the law of a carnal commandment, but after
  the power of an endless life.
  
  17 For he testifieth, Thou art a priest for ever after the order of
  Melchisedec.
  
  18 For there is verily a disannulling of the commandment going before
  for the weakness and unprofitableness thereof.
  
  19 For the law made nothing perfect, but the bringing in of a better
  hope did; by the which we draw nigh unto God.
  
  20 And inasmuch as not without an oath he was made priest:
  
  21 (For those priests were made without an oath; but this with an oath
  by him that said unto him, The Lord sware and will not repent, Thou
  art a priest for ever after the order of Melchisedec:)


So who is Melchizedek? Is he Jesus?

If he is not, how could there be priests of God before God chose himself a nation and defined priesthood after the Hebrews left Egypt?
Melchizedek was the King of Salem and a high priest of God.

Genesis 14:18-20
18 Then Melchizedek king of Salem brought out bread and wine. He was priest of God Most High,
19 and he blessed Abram, saying, “Blessed be Abram by God Most High,     Creator of heaven and earth.
20 And praise be to God Most High, who delivered your enemies into your hand.” Then Abram gave him a tenth of everything.

Although he was a priest of God, he was not Jesus.