This work addresses the relatively long setup latency and complicated network control and management caused by on-demand virtual network function service chain (vNF-SC) provisioning in inter-datacenter elastic optical networks. We first design a provisioning framework with resource pre-deployment to resolve the aforementioned challenge. Specifically, the framework is designed as a discrete-time system, in which the operations are performed periodically in fixed time slots (TS). Each TS includes a pre-deployment phase followed by a provisioning phase. In the pre-deployment phase, a deep-learning (DL) model is designed to predict future vNF-SC requests, then lightpath establishment and vNF deployment are performed accordingly to pre-deploy resources for the predicted requests. Then, the system proceeds to the provisioning phase, which collects dynamic vNF-SC requests from clients and serves them in real-time by steering their traffic through the required vNFs in sequence. In order to forecast the high-dimensional data of future vNF-SC requests accurately, we design our DL model based on the long/short-term memory-based neural network and develop an effective training scheme for it. Then, the provisioning framework and DL model are optimized from several perspectives. We evaluate our proposed framework with simulations that leverage real traffic traces. The results indicate that our DL model achieves higher request prediction accuracy and lower blocking probability than two benchmarks that also predict vNF-SC requests and follow the principle of the proposed provisioning framework.