#parent{
    height: 100%;
    width: 100%;
    overflow: hidden;
}

#child{
    width: 100%;
    height: 100%;
    overflow-y: scroll;
    padding-right: 17px; /* Increase/decrease this value for cross-browser compatibility */
    box-sizing: content-box; /* So the width will be 100% + 17px */
}