Mayhem sees off competition from Brandon Flowers and Hurts, who enter the Top 10 at numbers three and nine respectively.
May's 2008 release Love Tattoo climbs ten from number 14 into the top five.
Last week's number one, Katy Perry's Teenage Dream, drops one place to number two.
Elsewhere, Mercury Music Prize winners The xx see a mammoth 76-spot climb for their album XX.
This week's top ten in full:
1. (*) Imelda May - 'Mayhem'
2. (1) Katy Perry - 'Teenage Dream'
3. (*) Brandon Flowers - 'Flamingo'
4. (14) Imelda May - 'Love Tattoo'
5. (2) Eminem - 'Recovery'
6. (6) Jedward - 'Planet Jedward'
7. (5) Mumford & Sons - 'Sigh No More'
8. (4) Arcade Fire - 'The Suburbs'
9. (6) Hurts - 'Happiness'
10. (7) Lady GaGa - 'The Fame Monster'
> Click here for this week's Irish singles chart