Electrical dimmer switches for 4 switch locations?
There's more than one option!  

As ThreePhaseEel points out, Multi-location dimming is one option.  

However, depending on usage, specifically the case where the lights will mostly always dimmed at the same level or just having the dimming capability at one location with the existing switch still in operation at the other 3 locations. That is, you'll replace one of the existing 3-way locations, leaving remaining switches untouched.

If this is the case look for just ONE 3-way PRESET dimmer. 

One example: Lutron LED compatible PRESET dimmer: http://a.co/aIBfTR0 

(Ariadni, Toggler, Diva are all examples of preset in Lutron's product line) (Disclaimer, I don't work for Lutron. I do spec a lot of Lutron product for customers in my day job, as such I know the product lines--my only bonus for selling Lutron is the Lutron rep does take me to lunch 4 times a year.)

If dimmed the same all the time, this solution will be far less pricey than Multi-location, not to mention easier installation. 

The only con is that one of the existing 3way locations (not a 4-way) must be picked for the replacement dimmer. If you open up the existing and find the switch has 4 screw terminals, just stop and put it back together and move on to another location.  If the switch you take apart has 3 terminals then the PRESET dimmer can be installed in that location.

Here is a wiring diagram for a 4 location switching. In the diagram, the center two switches are the 4-way switches, the outer two switches are 3-way switches.