Who did the Chicago Bears play in the playoff of 1963?

Bobby Douglass.

The Cowboys and Bears played in the first game of the 1973 regular season with the Cowboys winning, 20-17. Douglass completed 6 passes in 13 attempts for 52 yards with 1 interception and had 13 rushing attempts for 57 yards. Cowboys QB Roger Staubach completed 9 of 21 passes for 91 yards, 2 TDs, and 2 INTs and had 7 rushes for 29 yards.

Douglass started 12 of the regular season games that season and Gary Huff started the other two.