The optical frequency sweep of an actively linearized, ultrabroadband, chirped laser source is characterized through optical heterodyne detection against a fiber-laser frequency comb. Frequency sweeps were measured over approximately $5\mathrm{THz}$ bandwidths from $1530\mathrm{nm}$ to $1570\mathrm{nm}$ . The dominant deviation from linearity resulted from the nonzero dispersion of the fiber delay used as a reference for the sweep linearization. Removing the low-order dispersion effects, the residual sweep nonlinearity was less than $60\mathrm{kHz}\mathrm{rms}$ , corresponding to a constant chirp with less than $\mathrm{15}\mathrm{ppb}$ deviation across the $5\mathrm{THz}$ sweep.