Sparse linear arrays (SLAs), such as nested and co-prime arrays, have the attractive capability of providing enhanced degrees of freedom by exploiting the co-array model. Accordingly, co-array-based Direction of Arrivals (Doas) estimation has recently gained considerable interest in array processing. The literature has suggested applying MUSIC on an augmented sample covariance matrix for co-array-based Doas estimation. In this paper, we propose a Least Squares (LS) estimator for co-array-based DoAs estimation employing the covariance fitting method as an alternative to MUSIC. We show that the proposed LS estimator provides consistent estimates of Doas of identifiable sources for SLAs. Additionally, an analytical expression for the large sample performance of the proposed estimator is derived. Numerical results illustrate the finite sample behavior in relation to the derived analytical expression. Moreover, the performance of the proposed LS estimator is compared to the co-array-based MUSIC.