This is a reasonable question, as there are limits around gold ownership depending on where you live. Numerous countries restrict the ownership of gold as it can be used to hide wealth.
However, these countries are usually found in the developing world as that is where the governments are unable to collect sufficient revenue.
In most Western nations, including the USA, there is no limit to private gold ownership. You can own as much as you like. All you need to keep in mind is how you will store it, and the costs associated with the storage.
That is not to say that things were always so good for gold owners. In 1933, President Roosevelt banned ownership of Bullion or the use of gold for monetary purposes. However, people were still allowed to keep up to $100 in gold (a huge amount at that time).