Always and since don't always work well together. Editor Emily Brewster comments:
The word always in "Since 1998, he has always been chair of the committee" is not necessary or idiomatic. This kind of construction is not unheard of in English, but it is very rare; in our database of citation text--which contains more than 100 million words--we have only 4 examples of this sense of since being followed by the adverb always in this way. Here's one of the four:
"Now, the protagonist is the main actor in something and has, since Greek times, always been used in the singular." (from Paradigms Lost by John Simon)
The original sentence you provided, "Since 1998, he has been chair of the committee," is perfectly good. "He has been chair of the committee since 1998" sounds even more natural.
"Since ten years ago, he has been chair of the committee" is technically correct, but again, not idiomatic. The since-phrase would more naturally come at the end of the sentence: "He has been chair of the committee since ten years ago." Even more natural would be "He has been chair of the committee for the past ten years."
