No, but it helps. The more accurate the birth time, the more detailed the chart. I've done readings for people who have no idea of their time of birth. The chart's calculated for noon. The houses, though, can not be calculated without a birth time, and they add much valuable data to a reading.
Birth certificates are the ideal source.
Check with your state records office, hospital or city of birth to see if it's on file. Don't just request a birth certificate as some don't have the time on it. Ask for a document that shows the time of birth. Parents, relatives and neighbors are another source of information. A family Bible may also have birth information in it.