We present results of a search for evidence of reentrance at high magn
etic field of the superconducting state in the quasi-one dimensional o
rganic superconductor (TMTSF)(2)ClO4, for a specific orientation of th
e field at low temperature. This search was motivated by the theoretic
al work of Lebed' and of Dupuis & Montambaux, and in part by that of T
esanovic and coworkers, who predict novel magnetic field-temperature p
hase diagrams in quasi-1-D and quasi-2-D superconductors in a strong m
agnetic field. In the quasi-1-D case, a field directed both normal to
the chains and along the layers is proposed to induce exotic oscillati
ons of the critical temperature at high field, while for the 2-D case,
quantum effects associated with Landau quantization lead to similar p
redictions. We have investigated the superconducting transition in a q
uasi-1-D candidate material, (TMTSF)(2)ClO4, to 0.06 K with field orie
nted along the b'-axis (+/-0.02 degrees). From mostly constant field t
emperature sweeps, we find positive curvature in H-c2(T) below about T
-c/2. In addition, a resistivity decrease is observed to persist to 7
T, the highest field employed, with a slightly positive slope partial
derivative H/partial derivative T above 5T. The possibility of these f
eatures being representative of high field superconductivity is discus
sed.