Two promising solutions have been recently proposed to address the massive growth in mobile traffic and wireless devices: LTE-U and in-band full-duplex (FD) wireless. LTE-U extends the benefits of LTE-A to the unlicensed 5 GHz band, used mainly by Wi-Fi users. However, the uncertainty in Wi-Fi user activities makes provisioning QoS guarantees to LTE-U users challenging. On the other hand, FD wireless can double spectrum efficiency by enabling simultaneous transmission and reception over the same frequency band. Our objective in this paper is to exploit excess capacity of deployed Wi-Fi networks (operating in the 5 GHz band) to orchestrate a 'robust' virtual LTE-U network from a hybrid set of half-duplex (HD) and FD Wi-Fi access points (APs). Although the orchestrated LTE-U network does not support deterministic QoS guarantees, it is designed to provide prespecified probabilistic QoS guarantees (hence, it is robust). Towards achieving our goal, we develop novel stochastic resource allocation formulations that optimally orchestrate a virtual LTE-U network from a hybrid set of HD/FD APs with the minimum cost. We first consider the single small-cell problem and propose a stochastic formulation, which we refer to as CCLTEUsingle. Then, we study the multi-cell stochastic allocation problem and develop another formulation, which we refer to as CCLTEUmulti. Our formulations adopt a 'chance-constrained stochastic programming' approach. We derive the deterministic equivalent programs of CCLTEUsingle and CCLTEUmulti and evaluate them numerically under various system parameters.