  We present a detailed spatially-resolved spectroscopic analysis of two X-ray
observations (with a total integration time of 73280 seconds) made of the
luminous northwestern rim complex of the Galactic supernova remnant (SNR)
G266.2-1.2 (RX J0852.0-4622) with the Chandra X-ray Observatory. G266.2-1.2 is
a member of a class of Galactic SNRs which feature X-ray spectra dominated by
non-thermal emission: in the cases of these SNRs, the emission is believed to
have a synchrotron origin and studies of the X-ray spectra of these SNRs can
lend insights into how SNRs accelerate cosmic-ray particles. The Chandra
observations have clearly revealed fine structure in this rim complex and the
spectra of these features are dominated by non-thermal emission. We have
measured the length scales of the upstream structures at eight positions along
the rim and derive lengths of 0.02-0.08 pc (assuming a distance of 750 pc to
G266.2-1.2). We have also extracted spectra from seven regions in the rim
complex and fit these spectra with such models as a simple power law as well as
the synchrotron models SRCUT and SRESC. We have constrained our fits to the
latter two models using estimates for the flux densities of these filaments at
1 GHz as determined from radio observations made with the Australia Telescope
Compact Array (ATCA). Statistically-acceptable fits to all seven regions are
derived using each model: differences in the fit parameters (such as photon
index and cutoff frequency) are seen in the different regions, which may
indicate variations in shock conditions and the maximum energies of the
cosmic-ray electrons accelerated at each region. Finally, we estimate the
maximum energy of cosmic-ray electrons accelerated along this rim complex to be
approximately 40 TeV. We include a summary of estimated maximum energies for
both Galactic SNRs as well as SNRs located in the Large Magellanic Cloud.
