I’m going to step back from sources to remind all who are reading of the person we are talking about, the God-man who humbled Himself from on high to powerlessly have Himself nailed to a tree for the love of all mankind. The Son of Man who said “let the little children come unto me” and “forgive them Father for they know not what they do.”
I’m positive Jesus is happy that you’re praying at all. You are His child, and He loves you. It matters not the hour of the day. If you can do it at three and you wish to do so, do so. But if you can’t, or you forget, remember you have a merciful, loving, kind Saviour. Mercy is in the name of the Chaplet.
However, if you still feel scruples in your soul, remember the diary says this:
“At three o’clock, implore My mercy, especially for sinners; and, if only for a brief moment, immerse yourself in My Passion, particularly in My abandonment at the moment of agony. This is the hour of great mercy… In this hour, I will refuse nothing to the soul that makes a request of Me in virtue of My Passion.” (Diary, 1320)
“If only for a brief moment,” He says. If you can’t get to the Chaplet right then (work, for instance), meditate on His Passion while doing your task as soon as you can, and then get to the Chaplet when you can. Jesus said this to give you His Mercy, not to terrorize you into following a specific time. No matter where your are, it’s always the three o’clock hour somewhere!