Is there proof of Christ’s exact birth date?

The day of Christ’s birth is virtually impossible to say with certainty. The tradition of December 25 is very old, however, dating back to Hippolytus (A.D. 165-235). Chrysostom (AD 345-407) also stated in AD 386 that December 25 was accurate, and hence it became the official position of the eastern church. From our vantage point, a midwinter date is quite acceptable and all objections can be met, but to be as specific as 25 December is beyond the material evidence. The year of his birth is probably either 5 or 4 B.C.