Additive for electrolyte and electrolyte and rechargeable lithium battery

A rechargeable lithium battery, comprising

• a positive electrode including a positive active material,
• a negative electrode including a negative active material, and
• an electrolyte comprising:
• a lithium salt,
• a non-aqueous organic solvent, and
• a first additive represented by the following Chemical Formula 1:
• wherein,
• R1 and R2 are independently C1 to C10 alkyl groups including at least one halogen,
• L1 to L2 are independently a single bond or a substituted or unsubstituted C1 to C10 alkylene group,
• L3 is a single bond or a substituted or unsubstituted C1 alkylene group, and
• R3 is a cyano group or a C1 to C10 alkyl group including at least one cyano group.