We consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp, and estimating its parameters (i.e., its initial frequency and frequency rate), given time samples of the observed signal. Common model order criteria select the number of harmonics based on the maximum likelihood estimator. We develop exact and approximated maximum likelihood estimators of these parameters. To avoid an exhaustive search in the initial frequency-frequency rate space involved by those estimators, we propose an alternative low-complexity two-step estimation method. The first step separates the signal to its harmonic components. Then, in the second step, the parameters of interest are estimated using least squares method given the phases of the harmonic components. The method is compared to the exact and approximated maximum likelihood estimators and to the well-known high-order ambiguity function based method. Numerical simulations and real data examples demonstrate that the proposed low-complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal-to-noise ratio. Since the estimates obtained by the proposed method achieve the Cramer-Rao lower bound at these signal to noise ratios.