"Mobile Suit Gundam UC" (Unicorn) is set in the Universal Century timeline, 96 years after the One Year War. The story begins in UC 0096, during a fragile peace between the Earth Federation and the remnants of the Principality of Zeon, known as Neo Zeon. The central conflict revolves around a mysterious artifact called Laplace's Box, said to contain a secret that could destabilize the Earth Federation's authority. The box's location is encrypted within a mobile suit, the RX-0 Unicorn Gundam, which is entrusted to the Vist Foundation, a powerful organization with ties to both sides of the conflict.

Banagher Links, a young student living in the space colony Industrial 7, becomes involved when he encounters Audrey Burne, a girl seeking to prevent the outbreak of war. Audrey is revealed to be Mineva Lao Zabi, the last surviving member of the Zabi family that once ruled Zeon. Banagher discovers his connection to the Vist Foundation and pilots the Unicorn Gundam, which activates in response to his Newtype abilities. The Unicorn Gundam is a prototype unit designed to unlock Laplace's Box, making it a target for both the Earth Federation and Neo Zeon forces.

As the story progresses, Banagher is drawn into a complex web of political intrigue and warfare. He faces off against Full Frontal, the charismatic leader of Neo Zeon, who pilots the Sinanju, a powerful mobile suit. The Earth Federation, led by figures like Captain Otto Mitas and Lieutenant Commander Riddhe Marcenas, seeks to suppress the truth of Laplace's Box to maintain control. Riddhe, initially an ally, becomes increasingly conflicted as his loyalty to the Federation clashes with his growing empathy for Banagher and Mineva.

The narrative explores themes of identity, legacy, and the cyclical nature of conflict. Banagher's journey is one of self-discovery as he grapples with his role in the unfolding events and his responsibility as a Newtype. The Unicorn Gundam itself evolves throughout the series, transforming into its awakened form, which symbolizes hope and the potential for change.

The series culminates in a climactic battle at the industrial colony of Palau and later at the abandoned Laplace space station, where Laplace's Box is finally revealed. The contents of the box challenge the legitimacy of the Earth Federation's governance, forcing all factions to confront the consequences of their actions. The resolution emphasizes the importance of understanding and reconciliation over perpetuating conflict, leaving a lasting impact on the Universal Century timeline.