Schala's Pendant

The Stone
Dreamstone, also known as Red Stone, Red Rock or Ruby, was a rare and highly valuable natural material since prehistoric times. According to Masa, only one pendant was made – along with a knife – out of this ancient red rock. The pendant was made by Belthasar and it was was experimental in time-warp technology. The knife was made by Melchior, who also re-forged the Masamune using more Dreamstone from prehistoric times.

 
During 12,000 BC the Royal family amassed enough red rock to make the Mammon Machine. Schala's pendant absorbed energy directly from the Mammon Machine, which in turn amplified her powers and allowed her to activate it. When she chants to channel magic through it, the blue jewel in the pendant glows.

The pendant was passed down through generations of royalty without magic power or knowledge of its true purpose. When inert, it would only react to time-related devices like Lucca's transporter. Only with energy from the Mammon Machine can the pendant be used for one of its original purposes – to open sealed doors with the machine logo on them or open chests with ancient family heirlooms that were likely sealed since the fall of Zeal.

The Dream
The pendant seems to have a mind of its own. In one scene after Crono's death, the Earthbound Village Elder found the pendant at Marle's (or the leading character's) side like a guardian. The pendant conveniently stays with specific people and causes specific timegates to be created at specific times. Crono's party believes that there may be someone, perhaps the planet itself, who wanted to change history. It's possible that 'dream' in dreamstone refers to the planet's dream.

The game makes it clear that Princess Nadia Guardia inherited the same pendant Schala had, as there was only one made. However, after the game changed history, Schala used the last of the pendant's power to save everyone. The pendant remains with her when she is stuck with The Mammon Machine and Lavos.

Schala's Amulets
In the first scene with Schala and Janus, she gives him a charm to protect him. This is nothing like Schala's pendant, however, it seems she is skilled at imbuing jewellery with protective properties. Janus continues to wear the Amulet into adulthood, when we realize that it protects the bearer's status in battle.

What happened to Schala and her pendant is somewhat explained in Chrono Cross. Schala had changed the pendant into a protective one and it now works like Gaspar's Chrono Trigger – the Time Egg used to save Crono. In life-or-death situations, the pendant would rewind time a little and send the owner into a safer point in the immediate past.