Yes, it is legal for U.S. citizens to own gold bars of any size, including 400 oz (also called “Good Delivery” bars, the standard used by the London Bullion Market Association).
This wasn’t always the case: from 1933 to 1974, the U.S. government restricted private gold bullion ownership under the Gold Reserve Act, with limited exceptions for jewelry, coins, and industrial use.
President Gerald Ford signed legislation in 1974 that restored Americans’ right to freely buy, sell, and hold gold bullion, effective January 1, 1975.
Today, there are no federal restrictions on owning 400 oz gold bars. The main practical hurdles are cost (worth roughly $1.3 to $1.4 million at current prices), secure storage, and liquidity, since these bars are typically traded between banks, refiners, and institutions rather than individuals.