Chain-link fences are easy to install and inexpensive to keep up, but there's one factor that chain-link fence users find to be rather difficult to deal with if they have a dog: climbing. The links in the fence provide nice little footholds for a pet trying to bound away to explore that interesting world on the other side of the fence, and other items in the yard can contribute to the jumping too. It is possible to keep a dog in a yard surrounded by a chain-link fence, but you have to be proactive.
Clean Up the Area Inside
Dogs are very good at identifying items that will help them gain altitude. Move everything but plants away from the fence. There shouldn't be any wood, toys, patio furniture, or anything else that the dog could use as a ladder or stepstool. Also take into account the dog's leaping skills. In other words, the dog could still get over the fence by making a huge jump from the top of whatever pile might be near the fence and gain enough air to sail over the fence. (Obviously, that's harder for small dogs to do, but large dogs often have enough jumping power to do that.) Move everything toward the house and away from the fence—there should be only lawn and plants by the fence.
Make the Outside Seem Less Appealing
Curiosity is often what drives dogs to climb over fences, so make your yard more appealing than whatever's on the other side of the fence. Have toys available and block the view outside the fence too. That could involve adding woven privacy strips to the chain-link fence or planting thick hedges around the yard that block the dog's view out.
Those privacy strips and plants also serve to block the footholds created by the links in the fence. If the dog can't place its paws in the spaces between the links, it can't comfortably climb up.
One more way to stop your dog from getting out, if not stop them from trying to climb, is to add a roller bar at the top of the fence. These have pipes that roll freely around a wire strung across the top of the fence. When the dog places a paw on the roller, it simply rolls around and makes the paw slip off. The dog can't find solid footing at the top of the fence, making climbing out much harder.
Older chain-link fence can be a problem because the links may have been bent out of shape, creating larger footholds that are easier for the dog to use. Have the fence repaired or replaced quickly to eliminate that problem.
Visit sites like http://www.lishmanfence.com to find fencing companies you can work with.