If there is only one person who makes up an LLC, is that person eligible to buy a group health insurance plan?

Being a registered LLC does not automatically qualify you for getting group insurance coverage. In most states, the company has to have a minimum of 3 employees, including yourself, before it qualifies for group health insurance rates, but some states require 5 or more. This means that a single person LLC would not be eligible for group insurance coverage on its own, but there may be other ways to get group insurance rates.

You can still get group coverage through some clubs and organizations, including AAA and AARP. Commercial organizations such as Sam's Club offer group health insurance rates to their members as well, and having an LLC will qualify for membership in that type of business oriented organization, giving you access to money saving purchases as well as benefits such as health insurance. Check with any civic or private organization you belong to as well, including such groups as the Rotary or Lion's Club, because some of them also allow members to have access to group health and life insurance.

Failing group insurance through organizations that you or your LLC belong to, your choices will be to either purchase individual insurance or look into qualifying for government sponsored Medicaid. The problem with those options is that individual insurance generally requires a strict medical examination and Medicaid will require your income to be at or near the poverty level. In the former case, if you qualify the rates will probably be much higher than with group coverage and in the latter case owning an LLC may automatically disqualify you, depending on the insurance laws of the state in which you live.