Soy sauce is not all the same. The dipping sauce with Hainanese chicken rice is dark soy sauce.
The soy sauce that is most well-known around the world is what we call "light soy sauce", or often just "soy sauce". This is liquid, about as viscous as water; a small amount of the sauce ranges from light to dark brown. It is predominantly salty.
"Dark soy sauce", on the other hand, is thicker, with a consistency like a very thin honey. It is also darker; even small quantities of the sauce are black. Its flavour is deeper than light soy sauce, and depending on the type and brand can have just a stronger umami flavour, or even taste slightly sweet.
External source if needed.
If you're hunting dark soy sauce, look for labels like "superior" or "aged" soy sauce. If the bottle is not opaque, you can verify by swirling the liquid around; dark soy sauce will coat the walls of the bottle, while light soy sauce will run down quickly.
And if you're specifically looking for a variant good with chicken rice, avoid those with added ingredients like mushrooms or scallops -- the flavour profile is wrong for the dish.
(Disclosure: I'm Singaporean, and proud of it.)