In this paper, we present a novel code-timing estimator for uplink asynchronous direct-sequence code-division multiple-access systems utilizing bandlimited chip waveforms. The proposed estimator requires only the spreading code and training of the desired user. We start from a maximum likelihood (ML) approach that models the intersymbol interference and multiple-access interference as a colored Gaussian process with unknown covariance matrix in the frequency domain. The exact ML estimator is highly nonlinear and requires iterative searches over multi-dimensional parameter space that is impractical to implement. To deal with this difficulty, we invoke asymptotic (large-sample) approximations of the ML criterion and reparameterization techniques, which lead to an asymptotic ML estimator that yields code-timing and channel estimates via efficient noniterative quadratic optimizations. To benchmark the proposed estimator, we provide Cramér-Rao bound analysis for the code-timing estimation problem. Numerical simulation results are presented, which show that the proposed scheme is resistant to interference, fading, and modeling errors (e.g., sampling position errors), and compares favorably to several competing schemes in multipath fading channels.