We report observations of the z = 3.87 broad absorption line quasar APM 08279+5255 (Irwin et al. 1998) with the Adaptive Optics Bonnette (AOB) of the Canada-France-Hawaii Telescope. The object is found to be a double source. The separation of the two images is 0.35" +/- 0.02" and the intensity ratio I_{north}/I_{south} = 1.21 +/- 0.25 in the H-band. No other image is detected down to H(5sigma) = 21.3 within 10" from the double image. Strong support for the lensing hypothesis comes from the uniformity of the quasar spectrum as a function of spatial position in the image obtained with the integral field spectrograph OASIS at CFHT. From the 2D-spectroscopy, narrow-band images are reconstructed over the wavelength range 5600-6200A to search for emission-line objects in a field of 15"x12" around the quasar. We find no such object to a limit of 6x10^{-17} erg cm^{-2} s^{-1}. We use the images centered on the deepest absorption lines of the Ly-alpha forest to dim the quasar and to increase the sensitivity closer to the line of sight. One of the images, centered at 5766.4A, exhibits a 3sigma excess 1.5" from the quasar to the north-east
