Christ is born!
Here is the Russian Cathedral Choir of Paris singing the kontakion for the feast of the Nativity:
Here are the troparion and some other hymns specific to the feast by an unknown choir:
Monachos has the texts for various hymns.
Troparion of the Nativity:
Thy Nativity, O Christ our God,
Hath shone upon the world the light of knowledge;
For thereby, they that worshipped the stars
Were taught by a star
To worship Thee, the Sun of Righteousness,
And to know Thee, the Dayspring from on high.
O Lord, glory be to Thee!
Kontakion of the Nativity:
Today the Virgin giveth birth
To Him who is above all being,
And the earth offereth a cave
To Him whom no man can approach.
Angels with shepherds give glory,
And magi journey with a star.
For our sake is born a young Child,
The Pre-eternal God!