Curious question. The manner you ask it suggests perhaps a lack of familiarity with watch terms, but the question itself implies big bucks to spend.

The Patek 3970 would not usually be called a "chrono". It may have the accuracy of a certified chronometer, but in this price range that is expected. Otherwise that term is for chronograph, which refers to a stop watch feature (even though it is not really a "graph" since it does not chart anything and should be termed a "scope", but chronoscope might sound too much like medicine for the icky parts).

The 3970 is a complicated calendar watch with day, date, moonphase and has a list price around that of a fully loaded 5 series BMW although an LNIB closer to a 3 series. Quite pretty and considered a good watch. It is probably at the upper range of the medium price Pateks (the upper tier at Patek Philippe begins at the price of a Z-8 and may increase by multiples of that car's list--all the way to a Ferrari F50).

You ask about a second hand piece. LNIB ones show up all the time (check Watchnet's banner dealers, Watchfinder's banner dealers, etc.), but it would help to get a 1 year warranty or a guarantee that the watch has been thoroughly serviced and works properly. Complicated watches mean major service when in need. If you get one that has not been well cared for it could be very expensive to fix (assume they all take months to service anyway).

If you need the day, date and moonphase the Patek may be a good choice. If you want something even more interesting at around the same price you might look at Audemars Piguet's Equation of Time (bearing in mind that it must be made for your timezone). If you want something that is more individually finished and assembled you could try Roger Dubuis complications (I believe they are usually in white gold). For something completely different, but horologically more fascinating and "upbeat" you might look into F.P.Journe's dual time (platinum only). For something that will have everyone gawking you might try Vianny Halter's Antiqua (platinum only). Lange is supposed to introduce its perpetual calendar early 2002 and it will probably cause the watch world to go crazy--since Lange's reincarnation it has been touted as the marque to "dethrone" Patek.

In Spring, you may want to see if you like the new Lange. And the time interval will allow you to learn more about other fancy brands. One shock I had in Hong Kong last month was seeing around 100 fancy watches in an afternoon and realizing how they all began to look alike (including all the Pateks), except for just a handful. You have an enviable search ahead. Have a good time at it.

Happy hunting and happy holidays.