The uncertainty in channel quality due to fading and shadowing along with the unpredictability of primary user (PU) activity make channel assignment in opportunistic spectrum access (OSA) networks quite challenging. In this paper, we propose two per-link channel assignment models under channel uncertainty: a static single-stage and an adaptive two-stage. In the static model, channel assignment is performed once, such that the rate demands are met with a probability greater than a certain threshold. This model is appropriate for a distributed network with no centralized spectrum manager. The adaptive model is a two-stage assignment model, where the initial assignment may be corrected once the uncertainties are partially revealed, such that the excess spectrum is returned back to the spectrum manager. This adaptive model is more appropriate when a centralized spectrum manager is available. Our channel assignment algorithms account for adjacent channel interference (ACI) by introducing guard-bands between adjacent channels that are assigned to different links. These algorithms aim at maximizing the spectral efficiency, considering the impact of guard-bands. The static ACI-aware channel assignment problem is formulated as a chance-constrained stochastic subset-sum problem (CSSP), and the adaptive assignment problem is formulated as a two-stage chance-constrained stochastic subset-sum problem with recourse (CSSPR). We develop heuristic algorithms for both models and test their performance. Preliminary results demonstrate that the proposed heuristic algorithms are highly efficient.