Q. If Jesus went right after his death to preach the good news to the “spirits in prison,” as 1 Peter describes, how could he tell the thief on the cross, “Today you will be with me in Paradise”?
We should indeed consider whether there is a discrepancy in chronology between Luke’s account of Jesus’ crucifixion and what Peter says Jesus did after he died on the cross.
Luke records how Jesus was crucified “along with two criminals—one on his right, the other on his left.” One of them began to mock him, saying, “Aren’t you the Messiah? Save yourself and us!” But the other one said he should keep quiet. “We’re being punished justly,” he insisted, “we’re getting what our deeds deserve. But this man has done nothing wrong.” Then this second criminal, often known as the “thief on the cross,” said to Jesus, “Remember me when you come into your kingdom.” Jesus responded, “Truly I tell you, today you will be with me in paradise.”
We know that all three men died that same day, because, as John explains in his gospel: “It was the day of Preparation, and the next day was to be a special Sabbath. Because the Jewish leaders did not want the bodies left on the crosses during the Sabbath, they asked Pilate to have the legs broken and the bodies taken down. The soldiers therefore came and broke the legs of the first man who had been crucified with Jesus, and then those of the other. But when they came to Jesus, they found that he was already dead, so they did not break his legs.”
So the plain meaning of Jesus’ statement to the criminal who defended him was that the two of them would be together in Paradise that same day after their deaths.
Peter, however, writes in his first epistle that “Christ also suffered once for sins, the righteous for the unrighteous, to bring you to God. He was put to death in the body but made alive in the Spirit. After being made alive, he went and made proclamation to the imprisoned spirits— to those who were disobedient long ago when God waited patiently in the days of Noah while the ark was being built.” This statement and some similar ones in the Bible have led to the doctrine of the “harrowing of hell,” that is, the idea that after his death, Jesus journeyed to hell, triumphed over it, and released its captives. (I affirm this doctrine in my post on this blog entitled, “What did Jesus do for three days after he descended into hell?“)
We should note, however, that it was actually not three days, as we would reckon that time period ourselves, between when Jesus died on the cross and when he rose from the dead. In the Hebrew idiom, today is the first today, tomorrow is the second day, and the day after tomorrow is the third day. The gospels record that Jesus warned his disciples in advance, “The Son of Man is going to be delivered into the hands of men; they will kill him, but on the third day he will be raised to life.” What he meant by that Hebrew expression was that he’d be killed and then after one full intervening day he would rise from the dead.
Sure enough, Jesus died on a Friday afternoon and rose on a Sunday morning. Even though we often speak of him being in the grave for “three days,” he was actually there for less than two days. Now the Bible also describes him leading the souls rescued from hell into heaven during that time. In Ephesians, Paul quotes from Psalm 68 and applies its words to Jesus: “When he ascended on high he led a host of captives.” Paul then asks, “In saying, ‘He ascended,’ what does it mean but that he had also descended into the depths of the earth?” So the understanding is that at some point after his death, but before his resurrection, Jesus led these rescued souls into heaven.
If we were going to assign an earthly time to an event that admittedly takes place outside of time, we would have to say that Jesus did this sometime between Friday afternoon and Sunday morning, since he didn’t have these people with him when he reappeared to his disciples. And if we wanted to coordinate this account with the conversation Jesus had with the thief on the cross, we would have to conclude that this thief must have been among the ransomed souls Jesus led into heaven after his crucifixion. If we wanted to be very particular about it, we would insist that this must have happened on Friday, since Jesus promised the thief, “Today you will be with me in Paradise.” (It does feel strange, however, to try to assign earthly times to events in heaven and hell.)
This may be the most we can say in response to this question. But let me leave you with one last thought. Jesus seems to have led both the criminal who defended him on the cross and large numbers of people who perished “in the days of Noah” up into heaven after his own death. He would no doubt have stayed there with them long enough to ensure their acceptance and welcome. (In that sense, the thief was indeed “with him in Paradise.”) But Jesus then returned to earth for forty days so that he could teach and instruct his disciples, to prepare them for their work of spreading the good news about him all around the world. This question about the thief on the cross, in other words, reveals that Jesus left heaven and came to earth for us not once but twice, first in his incarnation as a baby, and then again after his crucifixion in a resurrected body. We can only imagine that after dying on the cross, where he suffered so greatly, Jesus was ready to leave this world and never see it again. But instead, he returned to the very scene of his suffering, for the sake of those he had died for. As the old hymn says, “Hallelujah! What a Savior.”
Good Question 
There is another possible solution. See Thayer’s 3rd definition for paradise “3) the part of Hades which was thought by the later Jews to be the abode of the souls of pious until the resurrection: but some understand this to be a heavenly paradise.”
In other words, paradise was/is a Jewish synonym for “Abraham’s bosom” which was the part of hades/sheol/the grave where the righteous awaited resurrection. Jesus is recognizing that this thief showed faith.
How then do we explain Mathew 12:40 where it says the Son of Man will be in the heart of the earth three days and three nights.
As this post explains, “In the Hebrew idiom, today is the first today, tomorrow is the second day, and the day after tomorrow is the third day. The gospels record that Jesus warned his disciples in advance, ‘The Son of Man is going to be delivered into the hands of men; they will kill him, but on the third day he will be raised to life.’ What he meant by that Hebrew expression was that he’d be killed and then after one full intervening day he would rise from the dead.” The same explanation applies to the statement you cite.