the word 'bound' binds me

'bound' in this sense means he was heading that way...it's an archaic expression... "I'm bound for the Arctic on Sunday"... it's still used by us older people, but not much by anyone else.

Oh I see,

I thought It meant the chieftain was a chieftain of the highlands.

Since this poem is an extract from Lord Ullins daughter, would 'bound' here mean that the chieftain was heading for the highlands? Then where was he?

I think you know the poem.

No, it does not have that meaning. In this context, bound means travelling to, headed toward. It is not a form of the verb to bind, at least not in common usage, although it once may have been. (I checked, it was never related to the verb "to bind.")

Here is a verse from a "sea chanty," a song sailors would sing while working:

In South Australia i was born
Heave away, haul away
In South Australia 'round Cape Horn
We're bound for South Australia

It means that they are going to South Australia.

The Online Free Dictionary gives this usage a derivation from Old English (Anglo-Saxon) from a word meaning "ready," from an Old Norse word meaning "to get ready." I assume, as in to get ready to travel.

So, the chieftan in your example is going to the Highlands, the northern region of Scotland.

I don't believe you will ever see it used without the preposition "for"--you'll know this usage because you will see "bound for." Some other examples are "bound for glory," which is a somewhat figurative usage, found in Negro spirituals of the American South, and it means the speaker believes that he or she is going to heaven. Another usage, also figurative, is "bound for trouble," as in "She's bound for trouble." That means that the person referred to is will get into trouble, that she is headed for trouble.