At the time of its construction, Chain Bridge was considered to be one of the wonders of the world. Chief engineer Adam Clark, a master builder from Scotland, completed the span in 1849. Legend has it that he was so proud of his masterpiece he would challenge anyone to find any fault with his work. When it was discovered that the lions at either ends of the bridge didn't have tongues, he was so ashamed that he committed suicide. This of course is only an anecdote. The tunnel, which was built a few years later, is also the work of Adam Clark. By the way, the lions do have tongues; however, they are not visible from the street below.
Crossing the bridge is just a short walk and no matter which direction you go, the view is beautiful. It's also well worth a visit in the evening, when the bridge is all lit up. In the summer, festivals are held on the bridge almost every weekend.
http://visitbudapest.travel/guide/budapest-attractions/chain-bridge/