Many breeders and lovers of chihuahuas are starting to see more coat colors and patterns emerging. One of these is Lilac, and it is a beautiful color. However, many experienced breeders have no idea what this color is. This definition was taken from the Chihuahua Handbook, by D. Caroline Coile.
“Note, dogs with both b/b and d/d have a diluted tan gray color. This is appropriately termed lilac.” *1
This refers back to color genetics. The b/b makes the dog chocolate and the d/d makes the dog blue. When both of these are combined, the blue is diluted even further and has a chocolate sheen to the coat.

Looking at this example which is an actual pup from this breeder pair, you can see that the pup us neither chocolate like the father or blue like the mother.
Since this is two recessive genes, it is harder to breed than the blue or chocolate alone. Also, you should NEVER breed two lilacs together, just as two blues or two merles should never be bred together.
Also, if the dog has a wash (c/c) at the C locus then the lilac is diluted even further into what is called a lavendar or isabella color. We do not have a photo of this color yet. These dogs would be b/b, d/d, c/c.
Here is another photo showing the difference in the Chocolate, blue and lilac coat colors.

Here we have Kasey(blue merle) at the top, Hershey(chocolate, this was also while Hershey had eye surgery from a cat scratching his cornea, thats what the e-collar is for), Luna(blue) and Tequila(lilac) and the bottom.
More examples

Here is a blue on the left and a lilac with blue markings on the right. The little lilac has blue sabling and also a blue mask!


The lilac is on the right.


The lilac is in the middle of his two brothers, and then Lila full grown with a light lilac coat.

Here we have Lila (lilac) in the middle of her
brother Rico S. at the top and her mother Luna
on the bottom, the latter two are blue.

Lila (lilac), Hershey (chocolate), Luna (blue).

Luna (blue), Lila (lilac), Hershey (chocolate).

Luna (blue) and Lila (lilac).
Luna and Hershey are Lila's parents.
*1 The Chihuahua Handbook. D. Caroline Coile, Ph.D. Barrons Publishing, Hong Kong; 2000.