You could call a repair service, such as Furniture Medic etc., but you can probably re-glue them yourself. A Google search will turn up a number of articles that show how to do it.
Here's a link to one from howthingswork.com.

Here is a link that might be useful: chair repair

Reasonable price is impossible to say without seeing the chairs to know how much time and effort it will take to do the repair. But I'm sure than can be repaired. You may not get another 25 years out them however!

Finding chairs to go nicely with a 25 year old table is like finding a top to go nicely with a 25 year old skirt. Todays colors and finishes are different, and if you don't find it right away you could spend years looking and come up with nothing. We sell a LOT of casual dining and I see this day in and day out. Especially in your dining room you'll be more critical of the "match" than you would be for a kitchen set.

I'd like to talk you out of your mindset that replacing something 25 years old is a waste of money. I bet you'd really enjoy having a new set, probably more than you now realize.

Chairs often need to be disassembled and re-glued every 15-25 years. Pound for pound, chairs take more abuse than any other piece of furniture.

I do this work regularly and charge about $50 each to disassemble and re-glue chairs, including some incidental touch up work.

One of the major problems I have are the idiots that slam in 4 or 5 pneumatic brads in every joint. Other than that, the work is fairly routine and just time consuming.

If your library has this video, there's a good segment on chair regluing.

Here is a link that might be useful: Repairing furniture

My nephew and I repair furniture in client's homes. We definitely recommend having the chairs reglued. You'll get a lot more life out of them and "bobsmyuncle" is about right on the price. Considering what things cost today and the "cost" of finding a good match, you'll save tons by having them repaired. I don't recommend doing it yourself unless you have experience and tools. However, you may have a "handy" friend that can take on the job. Just remember to clean off all the old glue before regluing.

Since this thread bumped up to the top, there is an article on this. The "Chair Doctor" glue is what I use for the odd joint that I can't easily disassemble. Woodcraft also carries it, if you have one locally, you can save on shipping. Otherwise, I like good old white glue, like Elmer's or Titebond. It does not grab as quickly and allows you to get the chair all together and still have some time to wrestle it into a level-sitting position.

Here is a link that might be useful: Mag Ruffman does chairs