Jesus said:

Encourage souls to say the Chaplet which I have given you (1541). Whoever will recite it will receive great mercy at the hour of death (687). When they say this Chaplet in the presence of the dying, I will stand between My Father and the dying person, not as the just Judge but as the Merciful Savior (1541). Priests will recommend it to sinners as their last hope of salvation. Even if there were a sinner most hardened, if he were to recite this Chaplet only once, he would receive grace from My infinite mercy (687). I desire to grant unimaginable graces to those souls who trust in My mercy (687). Through the Chaplet you will obtain everything, if what you ask for is compatible with My will. (1731)

On another instance:

When a great storm was approaching, I began to say the chaplet. Suddenly I heard the voice of an angel: ""I cannot approach in this storm, because the light which comes from her mouth drives back  both me and the storm."" Such was the angel's complaint to God. I then recognized how much havoc he was to have made through this storm; but I also recognized that this prayer was pleasing to God, and that this chaplet was most powerful. (1791)

 

Prayed on ordinary rosary beads, The Chaplet of The Divine Mercy is an intercessory prayer that extends the offering of the Eucharist, so it is especially appropriate to use it after having received Holy Communion at Holy Mass. It may be said at any time, but our Lord specifically told St. Faustina to recite it during the nine days before the Feast of Mercy (the first Sunday after Easter). He then added: ""By this Novena, [of Chaplets] I will grant every possible grace to souls. (796) 

It is likewise appropriate to pray the Chaplet during the "Hour of Great Mercy" — three o'clock each afternoon (recalling the time of Christ’s death on the cross). In His revelations to St. Faustina, Our Lord asked for a special remembrance of His Passion at that hour. "