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There are a number of different insurance plans offered under the Affordable Care Act (Obamacare) which vary from state to state.

If the individual plan that you are in or want to be in meets the HDHP qualifications, then the answer is "yes". For the requirements, please see "High deductible health plan (HDHP)" at the IRS website.

Or just call the insurance company in question - they will know which plans, if any, are HDHP plans.