Despite the promising outlook, the numerous economic and environmental benefits of offshore wind energy are still compromised by its high operations and maintenance (O&M) expenditures. On one hand, offshore-specific challenges such as site remoteness, harsh weather, high transportation requirements, and production losses, significantly inflate the total O&M expenses relative to land-based wind farms. On the other hand, the uncertainties in weather conditions, asset degradation, and electricity prices largely constrain the farm operator's ability to determine the time windows at which maintenance is possible, let alone optimal. In response, we propose STOCHOS, short for the stochastic holistic opportunistic scheduler-a maintenance scheduling approach tailored to address the unique challenges and uncertainties in offshore wind farms. Given probabilistic forecasts of key environmental and operational parameters, STOCHOS optimally schedules the offshore maintenance tasks by harnessing the maintenance opportunities that arise due to a combination of favorable weather conditions, on-site maintenance resources, and maximal operating revenues. STOCHOS is formulated as a two-stage stochastic mixed integer linear program, which we solve using a scenariobased rolling horizon algorithm that aligns with the industrial practice. Scenarios are generated using a probabilistic forecasting framework which adequately characterizes the temporal dependence in key input parameters. Evaluated on a real-world case study from the U.S. North Atlantic where several large-scale offshore wind farms are currently being developed, STOCHOS demonstrates considerable improvements relative to prevalent maintenance benchmarks, across several O&M metrics, including total cost, downtime, resource utilization, and maintenance interruptions, attesting to its potential merit towards enabling the economic viability of offshore wind energy.