. . F+present the first measurement of the left-right cross sect ion as!mmetr! (ALR) for 2 boson production by eSecollisions. The measurement was performed at a center-of-mass energy of 91.55 GeV with the SLD detector at the SL.AC Linear Collider which utilized a longitudinally polarized electron beam. The a\.erage beam polarization was (22.4f0.7)%. U sin g a sample of 10,224 2 deca\x, ne measure ‘~LR _ @be 0.~00f0.044(stat.)f0.004(syst.) which determines the effecti\-e Lyeal; mixing angle to be sin2 t9$ = 0.2378 f O.O056(stat.) f O.O005(qxt.). Submitted to Physica. Revierv Letters +Th. IS supported in part by Department of Energy contracts: DE-FGO”-91ER40676 (BU), DEFG03-92ER40701 (CIT), DE-FG03-91ER40618 (UCSB), DE-FG02-91ER40672 (Colorado). DEFG02-91ER40677 (Illinois), DE-FG02-91ER40661 (Indiana), DE-AC03-76SF00098 (LBL), DEFG02-92ER40715 (Massachusetts), DE-ACO?-76ER03069 (MIT). DE-FGOG-85ER40224 (Oregon), -fiIjGAC$+Z6SF@515 (SLAC), DE-FG05-91ER40627 (Tennessee), DE-ACOS-76ER00881 (Wisconsin), DE-FG%-92ERi0704 (Yale); National Science Foundation grants: PHY-91-13428 (UCSC), PHI*-8921320 (Columbia), PHY-92-04239 (C incinnati), PHY-88-17930 (Rutgers), PHY-88-19316 (\;anderbilt), PHY-92-03212 (Washington); and by the Istituto Nazionale di Fisica Nucleare of It.aly (Bologna, Ferrara, Frascati, Pisa, Padova, and Perugia); the Japan-US Cooperative Research Project on High Energ] Physics (KEK, Nagoya, and Tohoku); the Natural Sciences and Engineering Research Council of Canada (British Columbia, Victoria, and TRIUMF); and the Science and Engineering Research Council of the United Kingdom (Brunel and RAL). This letter presents the first measurement of the left-right cross section asymmetry (ALR) in the production of 2 bosons by e+ecollisions. The measurement was performed in 1992 by the SLD Collabora.tion at the SLAC Linear -Collider (SLC). T&left-rightasymmetry is defined as [l], . . ALR =(a~ OR)/(~L +a~), (1) where CTL and OR are the e+eproduction cross sections for Z bosons (at the 2 pole) with left-handed and right-handed electrons, respectiveI!.. To leading order, the Standard Model predicts that this quantity depends upon the \~ctor (of ) and axial-vector (a,) couplings of the 2 boson to the electron current. . ALR= 2vdk = 2 [l 4 sin” O$] v$ + a: 1+ [l-4sin’t1$]” (2) where the effective electroweak mixing parameter is defined’ as sin’ 0;; F (1 ve/ae)/4. Note that ALR has the following properties: it is a sensitive function of -_ sin2b$, it is expected to be large (O.lO-0.15), and it does not depend upon the couplings df the 2 to its final states. We measure ALR by counting hadronic and T+Tdeca,ys of t,he 2 boson for each of the two longitudinal polarization states of the electroll b&am. The measurement requires knowledge of the a.bsolute beam polarization, but does not require knowledge of the absolute luminosity, detector a.cceptance, or efficiency [3]. _ -T&iLc. ~ as recently been upgraded to produce, a.ccelera.te, and collide a. spin-polarized electron beam [4,5]. P u ses of longitudina.lly polarized elect,rons are 1 produced by photoemission from a gallium arsenide cat.hode [6,7]. The helicity