MoTa allows you to move and pin your tabs with the keyboard. It is designed to supplement the excellent Vimium (other keyboard shortcut extensions are available), which unfortunately has no support for managing tabs this way. The shortcuts are vi-like.
Currently you cannot change the shortcuts for this extension, but if I get many requests for this (or for more friendly shortcuts) at email@example.com (two Ls), I will add this feature. I may also add command repetition (e.g. 3 moves current tab three to the right). Oh, and if Vimium adds this functionality, I will not use this extension myself.
: Move current tab to beginning of window
: Move current tab to end of window
: Move current tab left
: Move current tab right
: Move current tab out to new window
: Move current tab in to next window
: Pin/Unpin current tab