The discovery of the youngest Galactic supernova remnant (SNR) G1.9+0.3 has allowed a look at a stage of SNR evolution never before observed. We analyze the 50 ks Chandra observation with particular regard to spectral variations. The very high column density (N_H ~ 6 × 10²² cm^–2) implies that dust scattering is important, and we use a simple scattering model in our spectral analysis. The integrated X-ray spectrum of G1.9+0.3 is well described by synchrotron emission from a power-law electron distribution with an exponential cutoff. Using our measured radio flux and including scattering effects, we find a rolloff frequency of 5.4(3.0, 10.2) × 10¹⁷ Hz (hν_roll = 2.2 keV). Including scattering in a two-region model gives lower values of ν_roll by over a factor of 2. Dividing G1.9+0.3 into six regions, we find a systematic pattern in which spectra are hardest (highest ν_roll) in the bright southeast and northwest limbs of the shell. They steepen as one moves around the shell or into the interior. The extensions beyond the bright parts of the shell have the hardest spectra of all. We interpret the results in terms of dependence of shock acceleration properties on the obliquity angle θ_Bn between the shock velocity and a fairly uniform upstream magnetic field. This interpretation probably requires a Type Ia event. If electron acceleration is limited by synchrotron losses, the spectral variations require obliquity-dependence of the acceleration rate independent of the magnetic-field strength.