The word chamber is pronounced ˈtʃeɪmbə. For all the other words I can think of which contain the sequence <amb> the letter <a> represents the sound æ. Examples:
amber camber clamber gamble mamba ramble samba
Philip Taylor points out another word like chamber. It’s Cambridge = ˈkeɪmbrɪdʒ. And Petr Rösel adds chamberlain = ˈtʃeɪmbəlɪn.