While it is a chain shirt and thus normally a medium armor, what makes Elven Chain unique is that it can be worn by someone who isn't proficient with medium armor without imposing disadvantage on any ability checks, saving throws, or attack rolls that the wearer might make. This feature makes it an excellent choice for classes that typically don't have medium armor proficiency but could benefit from better protection, like some wizards or sorcerers.
However, to fully utilize its potential and not just avoid the penalties, proficiency in medium armor is indeed necessary. This allows the wearer to apply their proficiency bonus to the armor class (AC) calculations, which is an important aspect of effectively using any armor in D&D. This proficiency can come from the character's class, race, or certain feats that grant proficiency in specific types of armor.