.parent {
  width: 300px;
  height: 600px;
  overflow: hidden;
}

.child {
  width: 100%;
  height: 100%;
  overflow-y: scroll;
  padding-right: 17px; /* Increase/decrease this value for cross-browser compatibility */
  padding-left: 7px;
  box-sizing: content-box; /* So the width will be 100% + 17px */
}
.child a {
  width: 90%;
}