Do I get a second chance to believe in Jesus after I die? As if some people couldn't get far enough away from them on earth, several verses in the Bible seem to indicate that there will be preachers even in Hell.


  1 Peter 4:6 (ESV)
  For this is why the gospel was preached even to those who are dead, that though judged in the flesh the way people are, they might live in the spirit the way God does.


Does this mean that there will be a chance to repent and believe even after if I do not do so in this life?

Note: This is not a duplicate of Will there be a second chance for salvation after the Rapture? which talk about people who are still living on earth after the rapture (if there is such a thing). I am also not asking about the eternal nature of Hell. Whether it is or not is not the same thing as whether there will be a way to repent and be saved from there, although it does make more sense if Hell is indeed enternal.
John's revelation that he received while on the Isle of Patmos tells us that one day all of the dead that did not receive God while on earth must be judged according to their works. 


  REVELATION 20:11-15, KJV 11And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them. 12And I saw the dead, small and great, stand before God; and the books were opened: and another book was  opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their
  works. 13And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works. 14And death and hell were cast into the lake of fire. This is the second death. 15And whosoever was not found written in the book of life was cast into the lake of fire.


So what about the dead that did receive God while on earth? Jump back up to verse 4 to read that they will not be judged (Christ having already been judged in their stead), but judgment will be given to them.


  REVELATION 20:4, KJV And I saw thrones, and they sat upon them, and
  judgment was given unto them: and I saw the souls of them that were
  beheaded for the witness of Jesus, and for the word of God, and which
  had not worshipped the beast, neither his image, neither had received
  his mark upon their foreheads, or in their hands; and they lived and
  reigned with Christ a thousand years.


So to answer your question by scripture, no, there are no second chances to believe God. You have one chance to accept grace, and if rejected you must be judged by your works, and not by grace.