The first episode of the new psychological thriller aired at 9pm last night (Monday) after much hype from the critics.
And according to overnight figures, 3.53 million tuned in to its BBC 2 debut.
The ratings are expected to rise further once iPlayer views are taken into account.
The five-parter stars X Files actress Gillian Anderson and Co Down actor Jamie Dornan.
Anderson plays DSI Stella Gibson, an officer drafted in by the PSNI to help solve a grisly murder, while Dornan takes on the role of serial killer Paul Spector, who terrorises the women of Belfast.
Critics have compared the drama to Scandinavian hits like The Killing. The Guardian said: "Move over Denmark, Belfast is the new Copenhagen? Could be."
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