A very sensitive search for cosmic-ray antihelium was performed using data obtained from three scientific flights of BESS magnetic rigidity spectrometer. We have not observed any antihelium; this places a model-independent upper limit (95 % C.L.) on the antihelium flux of 6 × 10 −4 m −2 sr −1 s −1 at the top of the atmosphere in the rigidity region 1 to 16 GV, after correcting for the estimated interaction loss of antihelium in the air and in the instrument. The corresponding upper limit on the He/He flux ratio is 3.1 ×10 −6 , 30 times more stringent than the limits obtained in similar rigidity regions with magnetic spectrometers previous to BESS. PACS numbers: 98.80.Cq, 98.70.Sa, 98.80.Bp, 98.90.+s Cosmic-ray observations provide most direct evidence for our Galaxy being composed mostly by baryons. This baryon-antibaryon asymmetry can be global in the Universe, being created in the very early Universe due to the violations of CP and of baryon-number. However, depending on the nature of CP violation, baryon-symmetric models are conceivable [1] in which the Universe is separated into an equal number of matter-and antimatterdomains. Whereas γ-ray observations place strong limitations on the antimatter in our Galaxy and in the local cluster of galaxies, the domain structure could still exist beyond this scale. Although antihelium might be in principle produced in cosmic-ray interactions, their contribution to the He/He flux ratio is expected to be much smaller than 10 −12 [2]. Detecting antihelium at a level higher than this could therefore provide the evidence of antimatter domains or of other exotic phenomena such as superconducting strings in our Galaxy [3]. For further discussion of astrophysical considerations regarding the search for antihelium see the references [4,5]. We report in this letter (for more detail see [6]) a sensitive search for antihelium using the data from the '93, '94, and '95 flights of BESS detector, and provide model-independent upper limits on the absolute antihelium flux as well as on the He/He flux ratio. A limit on the flux ratio from an early analysis of '95 data is published elsewhere [4]. Fig. 1 shows front-and side-views of the BESS '95 instrument. The cylindrical configuration provides a wide tracking region and an acceptance of up to 0.32 m 2 sr depending on the off-line fiducial cuts. From inside to outside, it includes a jet-type drift (JET) chamber, in- * This work is dedicated to the memory of Dr. R. Golden.ner drift chambers (IDCs), a superconducting solenoid, outer drift chambers (ODCs), and a time of flight (TOF) hodoscope. The solenoid produces a magnetic field of 1 T with an uniformity of ±15% inside the bore.The JET chamber [7], as the key tracking detector, measures up to 24 points per track three-dimensionally, each with the resolution [8] of 200 µm in rφ plane and of 2 cm in z-position (a cylindrical coordinate (rφz) is determined by defining the magnetic field direction as z-axis). Each of the IDCs and ODCs consists of two 12-mmthick drift layers which are divid...