It was the practice of the Prophet (peace and blessings be upon him):
"He (peace and blessings be upon him) would pray witr at the beginning, the middle and the end of the night, in every part of it."
Hadith Referenceصحیح الجامع الصغیر / حرف الكاف / 5024
Hadith Gradingالألبانی:صحيح
Hadith Takhrij[حم] عن أبي مسعود. الروض النضير ١٠١٤.