To tackle the increasing global energy demand the climate change problem, the integration of renewable energy and negative emission technologies is a promising solution. In this work, a novel concept called "negative emission hybrid renewable energy system" is proposed for the first time. It is a hybrid solar-wind-biomass renewable energy system with biochar production, which could potentially provide energy generation, carbon sequestration, and waste treatment services within one system. The optimization and the conflicting economic and environmental trade-off of such system has not yet been fully investigated in the literature. To fill the research gap, this paper aims to propose a stochastic multi-objective decision-support framework to identify optimal design of the energy mix and discuss the economic and environmental feasibilities of a negative emission hybrid renewable energy system. This approach maximizes energy output and minimizes greenhouse gas emissions by the optimal sizing of the solar, wind, combustion, gasification, pyrolysis, and energy storage components in the system. A case study on Carabao Island in the Philippines, which is representative of an island-mode energy system, is conducted based on the aim of achieving net-zero emission for the whole island. For the island with a population of 10,881 people and an area of 22.05 km(2), the proposed optimal system have significant negative emission capability and promising profitability with a carbon sequestration potential of 2795 kg CO2-eq/day and a predicted daily profit of 455 US$/day. [GRAPHICS]