NOTE: This is a condensed excerpt from my forthcoming (2014) commentary on Philippians.
When Paul opens his letters, he always includes a description of himself. Here in Philippians 1:1 that description is servant of Christ. This translation is slightly misleading, since the Greek word doulos refers to a slave rather than a hired servant. This is one of Paul’s favorite titles, though it is phrased in a variety of different ways. The moniker reflects his conviction that he belongs to Jesus Christ and is completely at his disposal. It may also reflect Paul’s conviction that Christ dwelling in him was fulfilling the mission of the Servant of the Lord in Isaiah 49:6 to be a light to the nations, bringing salvation to them (cf. 2 Cor 5:20-6:2; Gal 1:10, 15-16; 2:20; Col 1:24-26; see also Acts 13:46-48). But Paul also applies the title “servant” to his coworkers in ministry, including Timothy as he does here (cf. also Col 4:12; 2 Tim 2:24-25). The prominence of the title may also stem from Jesus’ own teaching that those who desire to be great must be servants, following the pattern of Jesus himself (Mark 10:43-45). More importantly this title also anticipates the description of Christ in 2:7 as one who took “the form of a servant” in an act of self-sacrificial love for others. The work of the ultimate servant Jesus Christ creates servants who are empowered to love and live as he did.
Is the category of servant/slave at the heart of your self-identity as a Christian?
 For a helpful description of slavery in the Roman empire, see J Albert Harrill, “Slavery,” in Dictionary of Paul and His Letters (ed. Gerald F. Hawthorne, Ralph P. Martin and Daniel G. Reid; Downers Grove: IVP, 1993), 1124-27. On the spiritual significance of slavery as a metaphor for the Christian life, see Dale B. Martin, Slavery as Salvation: The Metaphor of Slavery in Pauline Christianity (New Haven: Yale University Press, 1990) and Murray J. Harris, Slave of Christ: A New Testament Metaphor for Total Devotion to Christ (NSBT 8; Downers Grove: IVP, 2001).
 This is most clearly seen in Galatians. For a fuller treatment, see Matthew S. Harmon, She Must and Shall Go Free: Paul’s Isaianic Gospel in Galatians (BZNW 168; Berlin: De Gruyter, 2010), 103-22. Of course, given the prevalence of slavery in the ancient world the Philippians would also have heard this description in light of that; see O’Brien, Philippians, 45; Fee, Philippians, 62-63.
 This idea of the work of the Servant of the Lord creating servants is drawn from Isaiah 40–66; see further Matthew S. Harmon, She Must and Shall Go Free: Paul’s Isaianic Gospel in Galatians (BZNW 168; Berlin: De Gruyter, 2010), 71-75.