The Icelandic band's current single 'Little Talks' spends a second week at number one in Ireland, while Rita Ora remains at two with 'How We Do (Party)'.
Florence + the Machine are up to three with 'Spectrum', Taylor Swift moves up to four with 'We Are Never Ever Getting Back Together' and Emeli Sandé's 'Read All About It' flies up to five.
Elsewhere, Lykke Li is up to eight with 'I Follow Rivers', Sam and the Womp land at 22 with 'Bom Bom' and Cheryl Cole's 'Under the Sun' advances to 24.
Justin Bieber's new single 'As Long As You Love Me' jumps 13 places to 28, Ed Sheeran is at 33 with 'Small Bump' and Gossip are at 39 with 'Move in the Right Direction'.
This week's Irish Top 10 is as follows:
1. (1) Of Monsters and Men: 'Little Talks'
2. (2) Rita Ora: 'How We Do (Party)'
3. (5) Florence + the Machine: 'Spectrum (Say My Name)'
4. (11) Taylor Swift: 'We Are Never Ever Getting Back Together'
5. (19) Emeli Sandé: 'Read All About It, Pt III'
6. (4) Calvin Harris ft. Example: 'We'll Be Coming Back'
7. (6) Owl City and Carly Rae Jepsen: 'Good Time'
8. (21) Lykke Li: 'I Follow Rivers'
9. (12) Nicki Minaj: 'Pound the Alarm'
10. (7) will.i.am ft. Eva Simons: 'This Is Love'
Watch the music video for Of Monsters and Men's 'Little Talks' below: