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Network slicing allows mobile network operators to open their physical network infrastructure platform to the concurrent deployment of multiple logical self-contained networks, i.e., network slices. In this paper we propose and analyze ONETS: an Online NETwork Slicing solution that (i) builds on the budgeted lock-up multi-armed bandit mathematical model and properties, (ii) derives its analytical bounds in our proposed extension for network slicing, (iii) seamlessly integrates into the 3GPP architecture, (iv) proves its feasibility through a proof-of-concept implementation on commercial hardware considering three network slices and (v) allows for the design of a low-complexity online network slice brokering solution that maximizes multiplexing gains.