Gary Gold’s men will be looking for their first win in the competition before they finish the pool stages with a trip to Dragons on Friday 2 February at 7.30pm.
Warriors currently find themselves in second place in Pool 3, four points behind leaders Northampton Saints.
There is plenty to play for as any of the four sides in Pool 3 can still qualify for the knockout stages.
Tickets for Warriors’ clash with Exeter Chiefs are available from £10 for Adults and £5 for Juniors by clicking here, visiting the Wrriors Ticket Office or calling 01905 459309.
Meanwhile BT Sport will be screening Gloucester Rugby’s clash with Ospreys in Round 3 as well as Newcastle Falcons’ visit to Bath Rugby.
In Round 4 Northampton Saints host Harlequins live on BT Sport before Wasps entertain Leicester Tigers in front of the cameras.
Anglo-Welsh Cup Fixtures
Saturday 27 January | Warriors vs Exeter Chiefs | 3pm
Friday 2 February | Dragons vs Warriors | 7.30pm