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We report a theoretical investigation analyzing the threshold modes of a concentric-circle-grating (CCG) distributed feedback laser with a radially chirped first-order Bragg grating. A numerical coupled-mode analysis of a chirped CCG laser shows improved azimuthal mode discrimination for chirped gratings with linear, quadratic, and square-root radial dependence. Negatively chirped gratings, in which the grating period decreases with radius, result in improved threshold discrimination between the circularly symmetric fundamental mode and higher order modes; positively chirped gratings, in which the grating period increases with radius, result in decreased threshold for higher order modes in general. Also, the intensity for the fundamental mode at the grating center can be reduced by an order of magnitude using linearly chirped gratings.