Can Two Players Play Battlefield 3 Online on One Xbox 360?
No. The Xbox 360 allows only one signed-in profile to connect to Xbox Live at a time. You cannot have two gamertags simultaneously online on the same console.
Alternatives
Split-Screen Offline:Battlefield 3 supports 2-player split-screen in Co-op Missions (spec ops) only — not multiplayer
Two Consoles: Each player needs their own Xbox 360, own copy of the game (or game share via home console), and own Xbox Live Gold subscription
System Link (LAN): Two Xbox 360s + Ethernet cable/switch + two discs → local multiplayer without Gold. Still 1 player per console
For true online co-op, a second console + Gold is required.