I am looking for a story or book that one of my teachers had us read
in class.  I think we read it in the mid to late 1980's.  It was a
short story, perhaps a shortened version of a longer book.  I do not
remember the title of the story or the author's name.

The story was set in the future, and the main character was deemed by
society or the government or something to be too intelligent, so he
had to go around wearing chains and weights and stuff like that … some
kind of theme to the book that everyone should be equal, and if
someone was too intelligent or superior in some way or better than
average than they had to wear chains or weights or something to offset
their superiority and make them more average.

The answer I'm looking for is either the title of the story or the
author's name.

Hello.

I believe that the story that you remember is HARRISON BERGERON (1961)
by Kurt Vonnegut, Jr.

In that story, set in the year 2081, anyone with any sort of
superiority is required by the government to wear "hindrances."

Intelligent people have to wear "mental handicap radios" that disturb
their thinking.

Graceful dancers have to wear sandbags.

People with strong vision have to wear special lenses to distort their
eyesight.


"The year was 2081, and everybody was finally equal. They weren't only
equal before God and the law. They were equal every which way. Nobody
was smarter than anybody else. Nobody was better looking than anybody
else. Nobody was stronger or quicker than anybody else. All this
equality was due to the 211th, 212th, and 213th Amendments to the
Constitution, and to the unceasing vigilance of agents of the United
States Handicapper General."
source: "Harrison Bergeron," hosted by nmsu.edu
http://web.nmsu.edu/~kmentor/law/harrison_bergeron.htm

A 1995 made-for-television film was based on the story. A video is
available from Amazon:
http://www.amazon.com/exec/obidos/tg/detail/-/6303801919/

search strategy: "harrison bergeron"
I've recognized the story based on your description

I hope this helps.