* Fiat to invest 1 billion euros if deal backed

* Deal calls for more flexibility on shifts, fewer benefits

* Most Mirafiori unions agreed the deal last month

Workers at Italian carmaker Fiat's (FIA.MI) historic Mirafiori plant were set to start the voting later on Thursday on an employment deal aimed at helping revive Fiat's fortunes at home.

Fiat has said it will invest 1 billion euros ($1.3 billion) in the loss-making plant to build new, high-end Alfa Romeo and Chrysler models in exchange for concessions from workers. Fiat owns 25 percent of Chrysler.

Chief Executive Sergio Marchionne has said he will take the investment abroad if a majority of workers reject a new contract involving more shifts and less benefits.

Union sources expect a majority of workers will ultimately back the new labour contract so they can keep their jobs.

If the 'no' (vote) wins where will we go? If the government says that Marchionne will do the right thing in leaving Italy, who will save us? Fiat worker Salvatore Nanni told Reuters TV.

Union representatives met workers as they entered the plant to explain the vote. A banner outside said: A terrorist is someone who sells his rights.

The deal has won praise among business leaders and has the backing of most unions. Prime Minister Silvio Berlusconi has given it his open support, saying on Wednesday Marchionne would have good reason to quit Italy if Mirafiori workers rejected his plan. [ID:nLDE70B28J]

But it has met fierce resistance from the leftist FIOM-Cigl union. It has said Marchionne, an Italian-Canadian who has made Fiat a top European turnaround story, is sacrificing constitutional rights to turn a profit.

Fiom leader Maurizio Landini said the battle over Mirafiori would not end with the two-day referendum.

For us the Fiat case remains open and in any case it isn't a problem that only affects workers at Mirafiori, he said after meeting workers at the plant.

Around half of Mirafiori's workers are unionised and Fiom represents around 23 percent of the workers at the plant.

The proposed deal, similar to one Marchionne clinched at Pomigliano in southern Italy, was essential to make Fiat profitable in Europe and also ensure the survival of the plants, UBS car analyst Philippe Houchois said.

The accord represents a new approach to labour relationships in Italy as it breaks with the tradition of relying on national contracts.

Mirafiori's 5,500 workers will begin voting at the start of the night shift at 2100 GMT on Thursday and continue through Friday.

Marchionne's plan for Mirafiori, Fiat's oldest plant and long a symbol of Italian industry, is part of his larger 20 billion euro Fabbrica Italia strategy to double domestic production by 2014 by raising productivity at car plants. ($1 = 0.7610 euros) (Writing by Lisa Jucca; Additional reporting by Ian Simpson; Editing by Dan Lalor, Greg Mahlich)