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General Information:
Here the word "us" refers to Paul and Timothy but not the Colossians. (See: rc://en/ta/man/jit/figs-exclusive)
God would open a door to us
Opening a door for someone is a metaphor for giving that person the opportunity to do something. Alternate translation: "God would provide opportunities for us" (See: rc://en/ta/man/jit/figs-metaphor)
open a door to us for the word
"make an opportunity for us to preach his message"
the mystery of Christ
This refers to the gospel of Jesus Christ, which was not understood before Christ came.
for which also I have been in chains
Here "in chains" is a metonym for being in prison, though Paul probably also was physically attached to a chain. Paul was in chains because he told people about the mystery of Christ. Alternate translation: "It is for proclaiming the message of Jesus Christ that I am now in prison" (See: rc://en/ta/man/jit/figs-metaphor)