We present results derived from the first multi-chord stellar occultation by the trans-Neptunian object (229762) 2007 UK126, observed on 2014 November 15. The event was observed by the Research and Education Collaborative Occultation Network project and International Occultation Timing Association collaborators throughout the United States. Use of two different data analysis methods obtain a satisfactory fit to seven chords, yielding an elliptical fit to the chords with an equatorial radius of R = 338 -10 +15 km and equivalent radius of R_eq = 319 -7 +14 km. A circular fit also gives a radius of R = 324 -23 +30 km. Assuming that the object is a Maclaurin spheroid with indeterminate aspect angle, and using two published absolute magnitudes for the body, we derive possible ranges for geometric albedo between p_V = 0.159 -0.013 +0.007 and p_R = 0.189 -0.015 +0.009, and for the body oblateness between eɛ= 0.105 -0.040 +0.050 and e = 0.118 -0.048 +0.055. For a nominal rotational period of 11.05 hr, an upper limit for density of rho = 1740 kg m-3 is estimated for the body.
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