The Solar Neighborhood XIII: Parallax Results from the CTIOPI 0.9-m Program -- Stars with mu>= 1"/year (MOTION Sample)

We present the first set of definitive trigonometric parallaxes and proper motions from the Cerro Tololo Inter-American Observatory Parallax Investigation (CTIOPI). Full astrometric reductions for the program are discussed, including methods of reference stars selection, differential color refraction corrections, and conversion of relative to absolute parallax. Using data acquired at the 0.9-m at CTIO, full astrometric solutions and $VRIJHK_s$ photometry are presented for 36 red and white dwarf stellar systems with proper motions faster than 1\farcs0/yr. Of these, thirty three systems have the first ever trigonometric parallaxes, which comprise 41% of MOTION systems (those with proper motions greater than 1\farcs0/yr) south of $\delta$ $=$ 0 that have no parallaxes. Four of the systems are new members of the RECONS 10 pc sample for which the first accurate trigonometric parallaxes are published here: DENIS J1048-3956 (4.04 $\pm$ 0.03 pc), GJ 1128 (LHS 271, 6.53 $\pm$ 0.10 pc), GJ 1068 (LHS 22, 6.97 $\pm$ 0.09 pc), and GJ 1123 (LHS 263, 9.02 $\pm$ 0.16 pc). In addition, two red subdwarf-white dwarf pairs, LHS 193AB and LHS 300AB, are identified. The white dwarf secondaries fall in a previously uncharted region of the HR diagram.