If you pass GO, do you collect 200 at the end of the turn or as you pass GO?
Original answer
You collect $200 each time you pass over or land on the GO. See the official rules.

Each time a player's token lands on or passes over GO, whether by throwing the dice or drawing a card, the Banker pays that player a $200 salary.
&quot;The $200 is paid only once each time around the board. However, if a player passing GO on the throw of the dice lands 2 spaces beyond it on Community Chest, or 7 spaces beyond it on Chance, and draws the &quot;Advance to GO&quot; card, they collect $200 for passing GO the first time, and another $200 for Advancing to it the second time by the instructions on the card.&quot;

Your question is quite interesting, it has been asked before here and here.
What I think, is that player should collect $200 only if passing GO in the clockwise direction or landing on it (also by advancing to or over the GO using card). The rules state that it is possible to collect $200 more than once in a turn, however in this case I think that the player in question should:

Collect $200 for passing GO.
Take the chance card, go back 3 spaces to Mayfair. Do not collect $200 for passing GO this time.
Collect $200 for passing  GO in the next turn.

I might be wrong though.

Edit
There were some good comments posted that made me think more about this particular situation. I'm making this edit to answer all of them comprehensively, hopefully. Sorry about the long post.
Pay a $10 fine or take a Chance
Comment from @ColinD made me look for more information about the card. I've found information on Wikipedia  that this card was omitted in U.S. editions since 1936. I'm assuming it wasn't ommited just in U.S. editions, since I've never actually seen this card in real life and I live in Europe.
This might be what makes things complicated here. As @ColinD suggested later, situation described in the OP's question might be the only way to achieve passing GO in the counter-clockwise fashion. Since the card allowing this to happen was omitted, there was no need to address this issue in the official rules - that's why they might not be crystal clear about this. I'm also afraid that looking at the rules from 1936 wouldn't solve this issue.
If you would like to learn more about the history of Monopoly game, take a look on this and this.
Authorities
I wasn't completely sure my answer was correct and there were some good points made by other users. So, I decided to contact authorities for consultation. This is what I was told.
Hasbro Customer Service
After contacting them by online form and describing situation (without mentioning my thoughts on how this should be resolved) I received following response:

Thank you for contacting Hasbro Customer Service regarding the rules
for Monopoly. I'm delighted to help!

The player collects $200 for passing GO. They can choose to ask for it as soon as they pass the space or at the end of their turn.
Either way, no matter when they ask for it, it's owed to them for
passing GO.

Players do not collect $200 for passing GO counter-clockwise.

Yes, the player should collect $200 again as they passed GO.


I hope this helps! Happy gaming!

Ok, so this answer doesn't provide much reasoning behind this, but the results of rules interpretation seem to be the same as mine.
Main Judge of the Polish Monopoly Championships
I've contacted Mr. Michael Stajszczak, who was the main judge in all editions of the Polish Monopoly Championships. He judged many other games in tournaments and made a fair amount of rules translation for different board games. Again, I didn't suggest any particular interpretation of the rules in this situation. This is what he replied:

If described situation was to happen in the tournament, the decision would be like this:
Player should immediately collect $200 for passing GO, before drawing Community Chest card. He doesn't collect money for passing over GO in backward direction. However in the next move,
when he will be passing GO again, he should collect another $200.

This is the way I understood the rules. However, @Johno made a good point that maybe the player shouldn't collect another $200 when passing GO on the following turn due to the The $200 is paid only once each time around the board clarification, because he's already had the return for completing that circuit. I've also asked Mr. Stajszczak about this interpetation of the rules:

Indeed, this sentence could be interpreted in more than one way.
However, I think it addresses different issue. This was to resolve the
situation where player finishes his move on the GO - so that he
won't get the money twice (first time for landing on GO and second
time for leaving it).
By the way, the quoted sentence isn't present in Polish set of the
rules. That's why this wasn't an issue in any of the Polish
tournaments. Unfortunately we can't ask the game designer about this
since he passed away.
Just in case of doubt, there was always an information in the
Championship rules that the game rules are as main judge interpets them.

I believe this is probably the best answer you could get for this situation. That's the way the issue would most likely be resolved in the official tournament.