McCoughtry had 18 points for Atlanta (3-4), and Erika de Souza had 13 points and 11 rebounds.
Elena Delle Donne, the league's leading scorer, had 26 points and 10 boards for Chicago (2-3). Courtney Vandersloot had 18 points, and Cappie Pondexter finished with 13.
McCoughtry and Roneeka Hodges scored 10 points apiece to help Atlanta to a 37-36 lead at the break. A 10-2 spurt at the start of the fourth gave the Dream momentum, but Chicago responded with a 9-2 run to tie it at 72 with 1:23 left.
Jacki Gemelos made her WNBA debut for Chicago and did not score in four minutes. The 26-year-old guard has suffered five ACL tears — four at Southern California, where she played for current Dream coach Michael Cooper.