A slick line lubricator was made up on top of a christmas tree with a nitrogen line made up to a side entry pump-in sub. The rig chicksan swivel joints and straight joints were rigged up from the christmas tree wing valve to the choke manifold. The christmas tree master valve was closed. The job task was to test the lubricator and lines through to the choke with nitrogen to 6500 psi. A JSA was conducted prior to the job. Once the pressure was applied, a straight line between the christmas tree and choke parted about 1-inch past the weld on the wing-half end. A safety chain was attached to all connections on all lines but the chain on the straight joint slid off due to a clean break. All personnel were clear and no one was injured. However, clearly this incident had a high potential for injury to personnel.