The Northern National League team is the lowest-ranked club in the competition and its reward for eliminating the championship team Reading is a home game against David Moyes’ Flying Hammers.
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The FA Cup match between Kidderminster Harriers vs West Ham United will be broadcast live on BBC.
The out-of-league team is the lowest-ranked team remaining in the world’s oldest cup competition after the championship team’s elimination, Reading, in the third round.
Sixth tier club Hammers will welcome the Premier League led by David Moyes at Ajjborough on Saturday 5 February at 12:30pm.
The game will be shown live on BBC One and BBC iPlayer.
It is one of six selections made in the fourth round of the weekend, two on the BBC and four on ITV. The action begins on Friday (4 February) when Manchester United welcome the Championship side Middlesbrough to Old Trafford.
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Boro coach Chris Wilder scored a surprise away win over United last season while in charge of doomed Sheffield United.
His last trip will be to face United live on ITV, at 8pm.
The next day sees two head-to-head matches, with the Kidderminster game in the afternoon before facing the entire Premier League on Saturday night. Spurs welcome Brighton and Hove Albion at 8pm, live on ITV4.
Sunday sees three matches live on TV. The match begins with Liverpool at home against Cardiff City. The Anfield meet begins at 12 noon on ITV.
Coverage then shifted to BBC One when Nottingham Forest hosted East Midlands rival Leicester City. Departure at City Ground at 4 pm.
The final match of the rounds sees the other remaining non-league team, Boreham Wood, travel to Bournemouth.
ITV4 will broadcast this match live, with kick-off at 6pm.
For Kidderminster, confirmation of their fourth-round match on TV would be a welcome boost to their coffers.
The match against the Hammers will be their eighth game in the competition, having started qualifying in September.
They have already raised £157,000 in prize money, but they can expect that total to rocket thanks to coverage on the BBC.
Speaking following the draw, Kidderminster chairman Russell Bean said: “I will take on one of the most respected British coaches at David Moyes, which is fantastic for me.
“I know he respects the competition, the lower league and West Ham are going up. What a draw.
“Hopefully we can write more history.”
As was the case in the third round, there are no replays, so final level encounters will roll into overtime. If necessary, penalties will determine the winners.
The third round saw eight matches go into overtime. Only one went the distance, with Queens Park Rangers beating Rotherham on penalties to book their place in the fourth round.
The full list of televised FA Cup fourth round matches
Friday 4 February: Manchester United – Middlesbrough, 8pm (ITV).
Saturday 5 February: Kidderminster Harriers-West Ham United, 12:30pm (BBC One).
Saturday 5 February: Tottenham Hotspur – Brighton & Hove Albion at 8pm (ITV4).
Sunday 6 February: Liverpool – Cardiff City, 12 noon (ITV).
Sunday 6 February: Nottingham Forest – Leicester City 4pm (BBC One).
Sunday 6 February: Bournemouth – Boreham Wood 6pm (ITV4).