1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Nf3 d5
4...c5 is the normal move in the spirit of the Nimzo-Indian Defense.
5.Qa4 Nc6 6.e3
6.Bg5 is almost as popular and is given in the first four lines of the Encyclopedia of Chess Openings. It may be of interest that in Chess Informant 10/600 Vladimir Sokolov judged 6.Bg5 as dubious, suggesting 6.e3. Perhaps 6.e3 is slightly more accurate than 6.Bg5. Even so, both moves have been played often.
Black to move
6...O-O appears to be the normal move here. My 6...Bd7 is the second most popular choice. Zoltan Gyimesi is the highest rated player who has played 6...Bd7 and he lost that game in a queen ending with most of the pawns remaining on the board and a nearly locked position.
It is hard to blame the opening for that loss. Nonetheless, the scoring percentage differences between 6...O-O and 6...Bd7 seem significant. White scores 55.6% over 411 games after Black castles. In the 55 available games with 6...Bd7, White's score jumps to 68.2%.
In my game, my position quickly grew poor with terrible piece coordination. My position was lost until my opponent blundered an exchange that led to an ending where I had a rook against a knight. All the pawns eventually came off and the game was drawn.
Is 6...Bd7 an inaccuracy, perhaps even an error? I think so.
6...Bd7 forces White's queen to move a second time due to the threatened discovery. 6...O-O steps out of the pin. Perhaps the queen then has less purpose on a4 and will be compelled to move again when Black's bishop is no longer a target.
Why is it an error? Does the bishop have a better square? It may. In games where Black castles, the bishop often goes to d7, but sometimes it goes to e6 or f5. In a few games, it takes up a position on b7. The major problem with 6...Bd7 is that it wastes time. Pieces should be placed on their best squares when they move for the first time. It is not clear in the diagram position where this bishop will be best placed. It is clear, however, that Black will castle kingside.