To advance the gospel
Paul revealed that he was now in custody in Rome. This news might have make the people of the Philippian Church anxious, but Paul himself was sure that his imprisonment would serve to advance the gospel. Maybe he rather actively let the whole palace guard or anyone else know why he was in chains - it was for Christ.
And behold, those who were united in Christ dared all the more proclaim the gospel without fear(1:14). The gospel will never be in chain, but spreads never to cease.