Yes, libertarians fully support the right to keep and own firearms. The right to bear arms, or the Second Amendment to the United States Constitution, is a cornerstone of libertarian beliefs.
The Second Amendment states that 'a well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.'
Libertarians fully support decentralized, private gun ownership and typically view all gun laws as an infringement.
This, however, does not mean that a libertarian must own firearms themselves. While it can be argued that it is responsible and an individual's "duty" to posses firearms, libertarians believe that it is your choice to own or not to own guns. There are libertarians who do not like guns and won't keep them in their homes, but fully support your right to do so. Supporting the inalienable right to own firearms is what matters most.
Why is the Right to Bear Arms So Important?
The right to bear arms is a foundational freedom, and extremely important for many reasons. A very basic freedom to protect ones own life and freedom is paramount. It is an inalienable right. No government on the planet has a right to disarm their people, and doing so is an act of tyranny and oppression, for they have stripped away the individual's basic human right to defend themselves and be free.
Beyond defense is the argument for private ownership and free agency that every human possesses. Outside of the necessity to defend your own life, it is your freedom to have private ownership of your possessions, whatever reason you choose to own them.
Defending against tyranny is an important reason to maintain the right to keep and bear arms. Once a government has stripped its citizens of the right to own guns, they cease to be citizens and are now subjects. "An armed person is a citizen, a disarmed person is a subject."
In a free society, the people have the right to keep and bear arms. Totalitarianism and authoritarianism run rampant in countries where the people have been disarmed. Allowing yourselves to be disarmed paves the way for autocratic control and iron-fisted rule, the very thing that America has fought against for hundreds of years.
We can run our lives better than the government can, and we must always preserve the natural right to own guns.
For these reasons, and many more, libertarians believe in the right to bear arms.
For more information, see What is Libertarianism?