Chrono Trigger > Chapter 23: The New King (12,000 B.C. second time)
Introduction
You begin this chapter after confronting Magus in 12,000 B.C. and just when you're able to fly anywhere you wish with the Epoch; you'll stay in this chapter until you rescue Crono. At this point, you can do any number of sidequests listed in Chapter 25: The Fated Hour, but this chapter is written with the assumption that you'll spend your time saving Crono first. If this is your first time through the game, you'll almost certainly want to complete the quest to save Crono before doing anything else, and if this is a New Game + you won't need the equipment that the other sidequests offer since you'll have them already. So I'll assume you're just going to proceed with getting Crono back.
You'll start out in 12,000 B.C., you can say hi to Alfador in the forest area if you want but Magus won't show any emotion. The Nu will also sell some new items in the center hut. Take to the skies in the Epoch, and you'll see the Ocean Palace rise into the sky, it will show up in all future time periods from this point on. For more details, see the next chapter. Head to the End of Time to talk to Gaspar.
Incidentally, Gaspar will have a special bit of dialogue talking to his old pupil if you talk to him with Magus in the party and without Marle. He'll play a song, "memories of Crono" and offer you a Time Egg, or a Chrono Trigger, which gives you the chance to alter history. To use it you'll have to go to Death Peak and have a clone of the person you want to save, but Gaspar will just tell you to visit Belthasar. Head to 1000 A.D. with the Epoch (fly around and hit Y to change time periods) and compete for a clone of Crono at Bekkler's lab if you don't have one already, and pick it up at Crono's house once he has one. After that, use the Epoch to fly to the Keeper's Dome and talk to the Nu there. Belthasar will have one final program to execute to help you climb Death Peak, then ask you to let the Nu sleep.
Also, talk to everyone at the end of time if you want to get their reactions to Crono being gone, and challenge Spekkio if you want, for me this was the first time I had a chance at winning the level 30-39 set. Keep in mind the form you fight depends upon the character in the lead of your party, which you can now select.
Death Peak
Challenging Lavos
If you challenge Lavos during this chapter (While you have the Epoch flying but before you rescue Crono), you'll get The Reunion Ending. There are several variations depending on whether or not you crashed the Epoch into Lavos, spared Magus, and whether or not you got the clone or the time egg. The basic theme of the ending is that Marle and company go back to rescue Crono at Death Peak since you didn't do it yourself.
Continue to Chapter 24: The Time Egg (2300 A.D. third time)