Chrono Trigger > Chapter 3: The Queen is Gone (600 A.D. first time)
Introduction
At this point you'll have both Crono and Lucca in your party. You should have gotten some cash from fighting monsters, so head to the market if you want and get some equipment, but otherwise your first goal will be to head into the cathedral. You should start getting used to using your different characters techniques to take out groups of monsters, as well as using double techs when you learn them which takes up both characters turns. Make sure you have some tonics, ethers, and revives if you want to be able to heal or restore your characters.
The Cathedral
Talk to each of the nuns, and talk to the upper left one then search where she stood to find the missing coral pin the king mentioned. Note that you won't be able to do this until you have Lucca in your party. The nuns will turn into Nagaettes, and you'll have to fight them off. A strange froggy character will show up to save you from a surprise attack, and you'll get a chance to name him and have him join your party. We'll call him Frog for simplicity's sake, although like four of the main characters in the game, that's not his real name anyway. Play the organ to open up a new door when you're ready.
Challenging Lavos
Impossible during this stage of the game since you have no access to a time gate.
Continue to Chapter 3: The Queen Is Gone (600 A.D. first time)