We report here the first study of proper motions of fast filaments in the young , oxygen-rich supernova remnant G292.0+1.8 , carried out using a series of [ O iii ] 5007 Å emission-line images taken over a period of more than 21 years . Images taken at seven epochs from 1986 to 2008 , all from telescopes at the Cerro Tololo Inter-American Observatory , show oxygen-emitting filaments , presumably ejecta fragments , throughout most of the remnant . We have measured the proper motions for 67 discrete filaments through two-dimensional correlations between images from different epochs . While the motions are small , mostly 20 to 100 \ > { mas\ > yr ^ { -1 } } , they are nevertheless measurable through a robust technique of averaging measurements from many epoch pairs . The data are qualitatively consistent with a free-expansion model , and clearly show systematic motions outward from a point near the center of the radio/X-ray shell . Global fits using this model indicate an expansion center at { R . A . } \ > ( 2000.0 ) = 11 ^ { h } 24 ^ { m } 34.4 ^ { s } , { Dec . } \ > ( 2000.0 ) = -59 \arcdeg 15 % \arcmin 51 \arcsec , and a kinematic age of 2990 \pm 60 years . The young pulsar PSR J1124–5916 is located 46″ southeast of the expansion center . Assuming that it was launched by the supernova , we expect the pulsar to be moving southeastward at 16 \ > { mas\ > yr ^ { -1 } } , or a transverse velocity of 440 \ > { km s ^ { -1 } } . We find the fastest ejecta along an axis oriented roughly N-S in the plane of the sky , suggesting that a bipolar explosion produced G292.0+1.8 , as appears to have been the case for Cas A .