The solution using <arrowscrollbox>. 

<tabbox>
  <arrowscrollbox clicktoscroll="true" orient="horizontal">
    <tabs>
      <tab label="aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"/>
      <tab label="bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb"/>
      <tab label="cccccccccccccccccccccccccccccccccccccccccccccccccccc"/>
    </tabs>
  </arrowscrollbox>
  <tabpanels>
    <label value="a"/>
    <label value="b"/>
    <label value="c"/>
  </tabpanels>
</tabbox>

When some of tabs are not visible, arrow-scroll-button is shown:

Note that arrowscrollbox element surrounds tabs element. If arrowscrollbox element is child of tabs element, tabbox does not work properly. 

<!-- Note: Does not work! -->
  <tabs>
    <arrowscrollbox clicktoscroll="true" orient="horizontal">
      <tab label="aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"/>
      <tab label="bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb"/>
      <tab label="cccccccccccccccccccccccccccccccccccccccccccccccccccc"/>
    </arrowscrollbox>
  </tabs>

Issue of this solution

On Mac theme, tabs are not painted properly:

Reference