Don't break your promise!

Literal

Promise [obj-を] don't-break [sentence-softener-よ].

A negative request/command built on ~ないで — the negative te-form used as an abbreviated request or command. Adding よ softens the tone from command to entreaty — the speaker is pleading rather than ordering. Typical of casual interpersonal speech where a full 破らないでください would feel stiff.