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 \farcs 0/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 \farcs 0/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 .