Direct sequence spread spectrum transmissions (DS-SS) are now widely used for secure communications, as well as for multiple access. They have many interesting properties, including low probability of interception. Indeed, DS-SS transmitters use a periodical pseudo-random sequence to modulate the baseband signal before transmission. A receiver which does not know the sequence cannot demodulate the signal. In this paper, we propose a method which can estimate the spreading sequence in a noncooperative context. The method is based on eigenanalysis techniques. The received signal is divided into windows, from which a covariance matrix is computed. We show that the sequence can be reconstructed from the two first eigenvectors of this matrix, and that useful information, such as the desynchronization time, can be extracted from the eigenvalues. Experimental results show that the method can provide a good estimation, even when the received signal is far below the noise level.