This paper considers the problem of estimating the bandwidth and the center frequency of a linear chirp signal from discrete-time noisy observations. The non-stationarity property of chirp signals implies that the signal has high rank and reduces the applicability of subspace based algorithms significantly. However, the special structure of the sample covariance matrix invites to use regular frequency estimation algorithms. We show how subspace type algorithms may be modified to provide accurate signal parameter estimates for linear chirp signals. The root-MUSIC algorithm is used as an example. Simulations compare the algorithm with a rank reduction method proposed by DiMonte and Arun (1990).