I will start this by saying it definitely isn't Chikorita. It has poor type matchups against 5/8 gyms, as well as Team Rocket. It's shallow move pool and bad defensive typing also doesn't help it at all.
Now that the trash is out of the way, we can debate real nuzlocke starters.
Cyndaquil is a solid choice, being fast to evolve and with good Sweeping stats and access to powerful STAB moves by level up, such as Flamethrower, Lava Plume, or potentially Eruption. It has a relatively easy time early game Clearing through Sprout Tower and Bugsy usually singlehandedly, and transitions well enough into late game, having only 2 true hard matchup, being Lance and Clair. It's flaw come from its also shallow move pool, making it more so just a 1 trick pony.
Totodile, in my opinion is the best starter for a nuzlocke in this vacuum. Water Typing alone makes it more viable then the other choices, considering this gens lack of a Grass or Electric specialist, As well as the generally weak selection of those typings available in this game. It can hit just as hard as Typhlosion late game with much better bulk for survival. But what really sets it apart from the other two is it's superior move pool. Capable of learning Bite and Ice Fang Early and Fighting/Ground/Rock coverage in the late game.
The caveat is their are so many good Water Types available, Namely Gyarados, Quagmire, and Tentacool to name a few. Gyarados in particular, is essentially a more powerful version of Feraligatr, filling all the same niches that Feraligatr does while having a superior ability and more powerful stat spread.
Typhlosion is much harder to replace, Fire types are often rare in the wild,and the selection this game isn't all that great with Ninetales, Rapidash, and Magmar, but if your playing HG, you can get access to Arcanine, a more well rounded Fire Type with better abilities.
TLDR while Totodile itself is a bit better then Cyndaquil, the wide array of good Water types available mitigates its advantage slightly. If you want your team to have a fire type, Cyndaquil is the answer, if you don't need a fire type, Totodile is the answer.
Hope this helps.