Chives die down naturally in autumn (fall) so if it's that time of year in your part of the world, then they're just doing what comes naturally.
If you want to keep them growing all year round, you'll have to take some indoors - check out the growing chives indoors section on this page.
If it's not that time of year, and your chive plants are in the garden and dying off, then they're either overcrowded or thirsty - they like lots of water.
So - give them a good drink first and see if they revive.
If that's not the case, then dig them up and look at the bulbs. Be careful when you're doing it, so that you don't damage the clump.
Very carefully, separate the bulbs. Keep the healthiest and replant them in clumps of three or four.
Keep them well watered and give them some tender loving care whilst they re-establish themselves.
If your chive plant is in a pot - then it's possible that they're overcrowded, dry or too wet.
Hmm.. well, overcrowded is easy - dry is easy too - but too wet?
Well - plants can be too wet and it's not always easily remediable - the soil beomes waterlogged and the plants can die.
This is easy to do in a pot and the symptoms of over or under watering are often the same - you can tell the difference by looking at the soil.
Take the chives out of the pot - if the soil is very wet then you're lucky it's chives - you can separate the bulbs from the soil and re-plant in new compost - if it had been another plant with one root system, then you might lose it.
Try and strike a happy balance - it's not easy if you're new to gardening, but feel the soil - if it's damp on top, then don't water - if it's dry on top, give the plants a little.
With experience, you'll soon learn what's enough.
