Children's Firearm Access Prevention Act - Amends the Brady Handgun Violence Prevention Act to: (1) define a "secure gun storage or safety device" to include one that is designed to prevent the firearm from being operated without first removing the device; and (2) prohibit any person from keeping a loaded firearm, or an unloaded firearm and ammunition, within any premise under such person's custody or control if that person knows, or with criminal negligence should know, that a juvenile is capable of gaining access to the firearm without the permission of a parent or legal guardian and fails to take steps to prevent such access.

Makes exceptions, such as in cases where: (1) the juvenile was supervised by a person older than 18 years of age and was engaging in hunting, sporting, or another lawful purpose; or (2) the juvenile gained the gun during a time that the juvenile was engaged in an agricultural enterprise.

Sets penalties for violations.

Directs the Secretary of the Treasury to ensure that a copy of the prohibition under this Act appears on the form required to be obtained by a licensed dealer from a prospective transferee of a firearm. Requires each licensed dealer to post the following notice in his or her place of business: "It is unlawful and a violation of the Children's Firearm Access Prevention Act to store, transport, or abandon an uninsured firearm in a place where children are likely to be and can obtain access to the firearm."