What is the value of a 1914 US 1 dollar Federal Reserve note?

These bills are actually Federal Reserve Bank Notes. While the distinction may seem to be semantic, the first official $1 FRNs were issued in 1963.

Unfortunately, like many older bills, it's not easy to provide an online evaluation because there are so many varieties - in this case, there were 39 possible signature combinations alone! Many of the bills are rare; prices for circulated ones can start at $800 and go up from there. A reputable dealer or appraiser who handles older paper currency should examine the bill in person.