There is something about the 1863 three dollar gold piece that has led to the preservation of several remarkable examples. Only 5,000 circulation strikes were made, and the date is rare overall. Q. David Bowers and Doug Winter offer these words in their series reference:  

{blockquote}'As the low mintage would indicate, the $3 gold piece is scarce in any grade and rare in higher levels. However, perhaps as many as several dozen Mint State coins exist, among which are some notable germs. Such showpieces are often candidates for extensive descriptions in auction catalogs and deservedly so. Among $3 coins dated dated in the 1860s, gems of 1863, while rare in an absolute sense, appear more often than do those of any other year. Most 1863 threes have very good eye appeal ... .      

'The true elusive nature of the 1863 is often overlooked, as low mintages also occur for most $3 coins of the 1880s, and those appear on the market with frequency. However, few 1863 coins were deliberately saved, and across the board they are quite rare.'{/blockquote}     

Aside from the obvious Civil War explanation, there is another likely reason that 1863 threes in high grade appear to have been saved in some small quantity: The 1863 quarter eagles were proof-only issues, and it may be that some people desirous of a nice gold coin from the year simply opted for the more-available three dollar denomination.