If I understand correctly, a self employed person can have an HSA, but can not deduct the contributions from taxes. Is that correct?

I am technically self employed even though I work for one client. I am a contractor and get a 1099, not a W-2. Is an HSA a good idea for me?

You are partially correct. A self-employed person can have a HSA, but cannot have "pre-tax employer contributions". You can take an above the line deduction for your HSA contributions and premiums that you pay.

As for whether this is a good plan for you, it depends on your situation, both medically and financially. If you a relatively healthy, with the income to cover the higher deductible, and if you stay that way for a few years, you can find yourself with a sizeable hsa fund account. This will allow you to purchase an even higher deductible, and in the process, reduce your premium costs.

As self-employed, you do as leevena notes, get an above-the-line deduction, but no deduction against the 15.3% self-employment tax.

Also, you might in fact be an employee of your 'one client'. That might allow you into a group health plan and any other benefit plans that the 'one client' has. You and your one client ought to run the facts of your situation passed the IRS (Form SS-8) to determine if you are actually an employee or independent contractor.