I started playing the Chigorin Defence in 1999 after I have discovered the (at this time) terrific book by Dunnington.
I still use it as my only weapon against 1.d4, and even at a higher master level it served me quite well. I frequently use it even against IMs/GMs, and last season in the German Bundesliga I drew GM Gabriel (in a winning position, grr), lost to GM Nyback (but only after I blundered in an equal position) and beat GM Krasenkov (2671).
I hope not to sound too confident (and I certainly do not want to brag with my results; I just want to give you an idea what a powerful weapon Chigorin can be), but I dare to consider myself an expert of this opening. Here are my two cents for the things already being mentioned.
First of all, I do think, too, that Black should play 2...Nc6! after 2.Nf3 - Although I do think that the best way for White to continue is 3.e3!? ... but I will cover this later.
Numerous possibilities have been mentioned here, which I will refer to one by one (Since 3.c4 transposes to main lines, I won't say anything about that in this topic):
3.Bf4 This line seems to be feared by some players, but just because it seems to be boring. Well, in a way it is, but in the same way it is just White giving up any hopes for an advantage. It is too much to describe the best setup, but I took the time to write a little summary with a few annotated games on my homepage. Unfortunately it is only in german, but it should be easy enough to understand. The link is:
http://www.schachmaterialien.de/Tschigorin/einleitungt0.htm 3.Bg5 I consider this a waste of time. Black can reply 3...f6! and obtain a good game. After 4.Bf4 Black gained a precious tempo after 4...Bg4 - f6 does not weaken the position but rather helps to support the important break ...e7-e5. White can't play 5.e3?? (5...e5 wins a piece) nor 5.Nbd2? (5...Nxd4 followed by ...e5 gives black an excellent game).
White can do 4.Bh4, but as already mentioned Black has the possibility of 4...Nh6 followed by ...Nf5. White is forced to retreat his bishop to g3, where it is harrassed by ...h5 (threatening ...h4). White will have to play h3 or h4 then, but after the trade on g3 the white pawn structure is severly crippled.
Finally it should be mentioned, that 3.e3!? is an interesting alternative. The idea is to play 4.Bb5! after 3...Bg4, with a possible threat of c4 followed by Qa4 and Ne5. Black has to play very carefully, I recommend a setup with ...e6 and ...Nge7 (do NOT develop the bishop to d6, it will have problems after a white c4), the bishop f8 is to be developed via g7. I haven't had much practical tests yet, but this looks interesting.