Some say that because French hens in the 16th century were very expensive, they represent the three gifts that the wise men brought, gold, frankincense, and myrrh. The cost today for just an ounce of all three would equal $1,375.32. We are not told how much of each the wise men brought to Jesus but just one ounce of each would have gone a long way back then.
Others say that it represents the Trinity, God the Father, God the Son, and God the Holy Spirit. In Matthew 28:19 we read; "Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit," Now in this verse we see the Trinity in that we are told to baptize in the NAME of the Father and the Son and the Holy Spirit. Name is in the singular form not plural. One person three names, kind of like a first, middle and last name.
The last reason is found in 1 Corinthians 13:13, known as the Theological Virtues. Look up this verse and record what these three virtues are and what we are told to do with them.