Very interesting question, the answer may vary depending on what it is you are pairing the customer and the contractor to do. For example do you want them just to be part of the team doing work for a customer or are you looking for something to be the back end of a productized service business website.
What you are describing sounds loosely like a project management system -- but it depends how much customizing you had in mind. There's not many solutions though that allow customization and the pairing process would probably a manual one. You'd review the customer's request, decide who the contractor would be and add them to the project -- if they will be working directly with each other, maybe you introduce the contractor in a message or task that you open up within the customer on the project.
That's one way to look at it, but if you are thinking of offering this as a service or have it fully customizable you may need to build something to meet that need. If so, then there may be some platforms to use as the foundation of it and extend it but those are probably more development frameworks not about collaboration. To provide more insight, it would be good to better understand more about the business model etc.
In the past, I have personally used a self-hosted project management system called activeCollab (http://activecollab.com) for exactly this type of thing --- I even built a business around helping others extend it. I would have recommended this as a potential option but recently they have switched directions and no longer offer the flexibility to customize via addons.
I'm currently looking at a lot of what's available now as an alternative -- many customers plan to stay with the current version and continue customizing, but others but others are looking for something in active development that will fit the need and still offer the customization options.
I could name a few software as a service project management / collaboration systems but there are so many out there to make the best recommendations it would be better to know more specifics about your needs but here's a few for example.
http://basecamp.com (paid, with free trial)
https://sprint.ly/ (well priced startup team package)
And the list goes on...
Here's a chart on Wikipedia of some -- almost everyday I learn about another project management system, and almost no two people agree on the best one :)
I'm not entirely convinced though that a project management system is the platform you are looking for --- I wonder if you are looking for something to provide a service to your customers maybe along the lines of something like http://wpcurve.com where customers hire them at a monthly rate for Wordpress tasks or a single engagement and then a contractor would be assigned to perform the work for the customer. I'm not sure what wpcurve.com uses or if the contractor is directly in contact with the customer but I'd guess they have something custom or are potentially using something more of a help desk software like http://zendesk.com and assigning someone to the support request as it's received. Just like project management there's several options in this space as well as self hosted options that can be customized. Now I'm curious, I may need to look into what they are using it if it's custom or a service like zendesk.
You may even find some CRM tools could work for this, like Streak.com which is an addon for Gmail. Or if your customers are purchasers of an app or and the contractors are support people then a tool like http://intercom.io would potentially work too. Again you may lose customizability if it's a software as a service solution but these might give you the opportunity to get up and running quickly or ggive you ideas about what it is you need -- if you do have to build a solution or find an alternative at least you know a bit about what you are looking for.
I hope this info is helpful as a start and if you can share more on your needs for the platform, I'd be happy to help.
Let me know if any of this helps get you on the path to what you need.