I actually think it is saying something rather different. Lawful characters do what they promise because they promised it, and any given lawful character can be relied upon to keep promises once they are made. On the other hand, Chaotic characters don't care what they promised, though any given chaotic character might coincidentally do what was promised provided there are reasons other than the promise to do it.Chaotic characters follow their consciences, resent being told what to do, favor new ideas over tradition, and do what they promise if they feel like it.
Emphasis mine, this would imply that an individual aligned with chaos can in fact be honorable... if he feels like it or if his conscience demands it. So it doesn't seem that honor is intrinsically tied to one's alignment
That's not being honourable. Being honourable means doing it even if you don't feel like it or it is contrary to your personal conscience - eg keeping your promise to a prisoner to spare his life even when you find out that he's the one who murdered your family.an individual aligned with chaos can in fact be honorable... if he feels like it or if his conscience demands it.
I actually think it is saying something rather different. Lawful characters do what they promise because they promised it, and any given lawful character can be relied upon to keep promises once they are made. On the other hand, Chaotic characters don't care what they promised, though any given chaotic character might coincidentally do what was promised provided there are reasons other than the promise to do it.
The contrast being presented in the PH is between "following their consciences" (Chaos) and "acting as society directs" (Law) -- or put another way, what you do when your impulses diverge from others expect. It doesn't mean you can hold any set of beliefs and still be considered chaotic provided you are true to whatever those beliefs happen to be.
That's not being honourable. Being honourable means doing it even if you don't feel like it or it is contrary to your personal conscience - eg keeping your promise to a prisoner to spare his life even when you find out that he's the one who murdered your family.
Also what @jsaving said in the post above this one.
Huh. Your right. So if my character's conscience tells him to always behave in an honourable fashion, what distinguishes me from lawful good?
For the two-dimensional alignment system to make sense, Good/Evil and Law/Chaos have to be reflecting fundamentally different things (if it were not so then one may as well boil it down to a single dimension). So you are absolutely right that being honorable doesn't make a character Good within the context of the game.
It does, however, make him Lawful (which I think is the point Hussar was trying to make).
Can a Chaotic character take honorable actions from time to time? Sure. Just as he doesn't have to automatically and reflexively oppose everything an authority figure says, or automatically and reflexively flout every tradition he can find, he doesn't have to maximize the number of lies he tells or the amount of poison he uses. But having one's actions sometimes coincide with what an honorable person would do is a far cry from actually being honorable, i.e. living by a code that says you won't lie/cheat/poison even when it would be convenient for you to do so.
Great honor is accorded whoever...
Takes from those who are not our people whatever they are strong enough to claim.
Leaves nothing of the weakling civilizations in our wake but fire and ash.
Attacks their enemy with wild abandon and reckless rage.
Does this "code" make the reaver/barbarian/whatever lawful... does it promote the aims and goals of the cosmic force of law in the world? I would say no to both of these questions... In fact it seems to actively serve and create chaos... and yet a warrior who did these things would follow a code and would be considered honorable in his particular society.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.