We present the first X-ray spectrum obtained by the Low Energy Transmission Grating Spectrometer (LETGS) aboard the Chandra X-ray Observatory. The spectrum is of Capella and covers a wavelength range of 5-175 A (2.5-0.07 keV). The measured wavelength resolution, which is in good agreement with ground calibration, is $Delta lambda simeq$ 0.06 A (FWHM). Although in-flight calibration of the LETGS is in progress, the high spectral resolution and unique wavelength coverage of the LETGS are well demonstrated by the results from Capella, a coronal source rich in spectral emission lines. While the primary purpose of this letter is to demonstrate the spectroscopic potential of the LETGS, we also briefly present some preliminary astrophysical results. We discuss plasma parameters derived from line ratios in narrow spectral bands, such as the electron density diagnostics of the He-like triplets of carbon, nitrogen, and oxygen, as well as resonance scattering of the strong Fe XVII line at 15.014 A.