  Our calculations have shown that the 5f_5/2-7s_1/2 23131 cm^{-1} transition
from the ground state in the ion Th^{3+} is very sensitive to the temporal
variation of the fine structure constant alpha (q=-75300 cm^{-1}). The line is
very narrow, the ion has been trapped and laser cooled and the positive shifter
line 5f_5/2-5f_7/2 4325 cm^{-1} (q=+2900 cm^{-1}) may be used as a reference. A
comparison may also be made with a positive shifter in another atom or ion.
This makes Th^{3+} a good candidate to search for the alpha variation.
