The Naga (ミアンヌ Miannu?, Mianne) (also known as Naga-Ette in the SNES/PS version) is an enemy in Chrono Trigger that first appears in the Cathedral in 600 AD. They can also be fought in Guardia Castle when Marle and the party are trying to prove King Guardia XXXIII's innocence. They also have a bromide dedicated to them, which might be of some interest to a lonesome old man somewhere...
Naga have two types of attack. One is "Scratch" (ひっかき?), which is just a physical attack. The other is "Nagamour / Slow" (ミアンヌの♥♥♥ / スロウー , Mianne's ♥♥♥ / Slow?) (also known as Naga-ette's (Heart symbol) / Slow spell! in the SNES/PS version) which causes the Naga to blow a kiss, sending a heart mark which inflicts both a small amount of damage and the slow status to a single party member, causing their ATB gauge to fill at reduced speed. They have fairly high HP and physical defense for the early game, but are weak to Fire and Lightning magic. However, players do not yet have access to magic spells at this point in the game, so to fully capitalize on their weakness players will either need to use Lucca's Flamethrower Tech to attack a single one, or Crono and Lucca's Fire Whirl Double Tech to attack a group of them.
Note that for the first fight against the four Naga in the entrance to Manolia Cathedral, if Lucca hasn't fought in many (or any) battles (which is quite likely since she joins the party just before in Guardia Castle) then she won't have access to Flamethrower (and thus, the double tech Flame Whirl will be inaccessible as well), so it might be a good idea to head to Guardia Forest for a few short battles to gain access to the Flamethrower and Firewhirl techs before taking on Manolia Cathedral to make this fight easier, though this isn't strictly necessary.