The Zamaretto League club, from near Bristol, reached the competition proper for the first time with a 3-0 win over Chippenham in the fourth round of qualifying yesterday, and were rewarded with a clash against the three-time former semi-finalists.
Another notable tie will see former semi-finalists Oldham face 1972 winners Leeds at Boundary Park, in an all-League One clash.
Blue Square North side Northwich Victoria will have home advantage against League One promotion hopefuls Charlton, while MK Dons manager Paul Ince will see his current team take on his former club Macclesfield.
Colchester, third in League One behind Leeds and Charlton, must visit Blue Square South Bromley. League Two leaders Bournemouth will face Chesterfield, and Southampton face a tricky trip to Bristol Rovers.
In matches between league and non-league teams, there may be potential for upsets as Gateshead host Brentford, Bath travel to Grimsby, York tackle Crewe, Sutton United take on Hereford, and Nuneaton Town play Exeter.
Stourbridge will fancy their chances at home against Walsall, Staines Town will relish the trip to Shrewsbury, and Wealdstone will have a home crowd behind them when they face Rotherham.
FA Cup first-round draw: Gillingham v Southend, Grimsby v Bath City, Gateshead v Brentford, Chesterfield v Bournemouth, Blyth Spartans or Telford United v Lincoln, Stockport v Tooting & Mitcham United or Eastbourne Borough, Burton v Oxford City, Barrow or Chester City v Eastleigh, Oldham v Leeds, Lincoln United or Cambridge United v Ilkeston Town, York v Crewe, Wycombe v Brighton, Hereford v Sutton United, Nuneaton Town v Exeter, Bristol Rovers v Southampton, Carlisle v Morecambe, Forest Green v Mansfield, Oxford United v Yeovil, Paulton Rovers v Norwich, Swindon v Woking, Port Vale v Stevenage, Luton v Rochdale, Bromley v Colchester, Accrington v Farnborough or Salisbury City, Millwall v Crawley Town or AFC Wimbledon, Stourbridge v Walsall, Shrewsbury v Staines Town, Wealdstone v Rotherham, Torquay v Cheltenham, Barnet v Darlington, Notts County v Bradford, Huddersfield v Dagenham & Redbridge, MK Dons v Macclesfield, Rushden & Diamonds v Hinckley United, Northwich Victoria v Charlton, Aldershot v Bury, Wrexham v Gloucester City or Lowestoft, Hartlepool v Kettering or Redditch United, Tranmere v Leyton Orient, Northampton v Kidderminster or Fleetwood.
Matches to be played on the weekend of November 7-8.