A Strength check is appropriate.
Strength Checks, PHB, p. 175
A Strength check can model any attempt to lift, push, pull, or break something ...
Ability checks are not saving throws, and proficiency with an ability's saving throws is independent of any bonuses to ability checks. There is no such thing as being "proficient in Strength"; there is proficiency with Strength saving throws, and there is proficiency with the (strength-based) Athletics skill.
Some class features may add part of the proficiency bonus to some unskilled ability checks -- see the Bard's Jack of All Trades feature (PHB, p. 54) and the Champion fighter archetype's Remarkable Athlete feature (PHP, p. 72). Both of these would apply to breaking the lock on a chest.
Generally speaking, saving throws are used to avoid or mitigate the effects of a spell, attack, or hazard. Characters usually don't initiate actions that succeed or fail on the basis of their own saving throw.