Popular media for Mycobacteria are Middlebrook (7H9 broth or 7H10 agar) or Lowenstein-Jensen.
For the slower growing mycobacteria it is necessary to supplement with antibiotics such as PANTA, but for your work this may be not needed, especially if you are not working with clinical or mixed samples.
You may chose the classic Middlebrook or Lowenstein-Jensen,but believe me that simple medium as TSA or BHI are also siutable for cultivation of Mycobacteria chelonae. I got good results using these ones. Only after appearance of colonies,check one of them by dying with Ziehl-Neelsen method to be sure of correct result.
The commonly used media to grow mycobacterium chelonae would be 7h9 broth medium, 7h10 agar or LJ medium (as detailed in the ATCC recommendation document attached).
I also agree that your mycobacteria will also grow well in BHI broth and agar.
Just be aware that some M.chelonae clinical isolates grow better at 30C (weak growth at 37). the middelbrook media (liquid or solid) or LJ give best results for this rapid growing mycobacteria. If you are looking to isolate M. chelonae from patients or unknown source do both incubations (30 and 37 C)
Löwenstein-Jensen medium at 37 degrees Celsius produces rough or smooth, nonpigmented colonies after 3 to 5 days of incubation.
MacConkey Agar without Crystal Violet can also be used most especially in differentiating M. chelonae and M. abscessus (since they are almost the same) from other nonchromogenic, rapidly growing Mycobacteria.
Egg-based medium is also used since in young cultures it may yield a negative niacin test result. Eg-based medium provide a consistent result.
and lastly, Middlebrook media (7H9 broth or 7H10 agar) as there are some species of Mycobacterium that grows better in liquid medium.