Call of Duty 4: Modern Warfare (Xbox 360) Supports 2-Player Split-Screen — Local Multiplayer Only

Yes. Call of Duty 4: Modern Warfare (2007) on Xbox 360 supports 2-player split-screen in:

• Local Multiplayer: Versus modes (Team Deathmatch, Free-for-All, etc.) on LAN/System Link or same console.
• Co-op Missions: Not in the base game. The campaign is single-player only. (Co-op campaign arrived in Modern Warfare 2's Spec Ops.)

Requirements

• Two Xbox 360 controllers (wired or wireless)
• Second profile (guest or signed-in)
• Start Multiplayer → Split Screen → Player 2 presses Start

Note: Split-screen reduces resolution/frame rate. Online matchmaking with a guest is restricted—typically System Link or custom matches only.