When is it safe to get facial fillers after a chemical peel?

Generally speaking a week should be fine after a chemical peel. I would just check with your treating physician and make sure that your skin is completely healed from the chemical peel before your injections.  Best, Dr. Green

If you are getting a 25-30% TCA chemical peel, this is considered a moderate peel. Depending on the health of your skin, you may flake and peel for up to 2 weeks after this type of peel. In my practice, I  have my patients using Alastin's Regenerating Complex for a full two weeks prior to the peel and as part of the post-peel process because I have found that this shortens the amount of downtime. [Peeling and flaking]. 
I mention this because peels work on the skin layers and fillers deal with structure. Depending on the type of filler and the location treated, there may be some bruising and swelling post filler treatment. So, while it is "safe" to do fillers at anytime, including the day of the peel, most individually will not be able to properly care for the treated area if the skin has been injured. I routinely recommend that patients ice the face after fillers, this may be uncomfortable if the skin is flaking and peeling. So, my general "rule of thumb" is you can have fillers as soon as you can ice your face comfortably... so the average time to wait is 7 days.
That said, peels do cause collagen remodeling and "plumping" of the skin, so if you only need some mild plumping, you may want to wait 3-6 months. The peels may achieve the results that you are looking for.