* Real the sole gainer in Latam * Chile"s peso flat after rate hike rally * Petrobras up as Bolsonaro considers privatization By Ambar Warrick Oct 14 (Reuters) - Brazil"s real rose on Thursday as data showed service sector activity grew more than expected, while most other Latin American currencies were muted as U.S. economic data fed bets on early tapering by the Federal Reserve. The real added 0.2% and was the sole gainer in Latin America, recovering from near six-month lows after services activity grew 16.7% in August from last year, indicating some resilience in the economy. "We expect some of the COVID impacted services sectors to recover further in coming months in tandem with further progress on the COVID vaccination program, reopening of the economy, and renewed fiscal stimulus," Goldman Sachs analysts wrote in a note. "However, accelerating inflation, rising interest rates, heightened political noise and policy uncertainty, and the interruption of the uptrend in consumer and business confidence may cap the upside." Latin America"s largest economy and most emerging markets are under threat from heightened inflation, which is likely to negate any momentum in an economic recovery. Rising fuel prices, global supply chain disruptions and an energy shortage are all poised to feed into inflation, and have dented sentiment towards emerging markets in recent weeks. Chile"s peso fell 0.1% after jumping 1% on Wednesday, when the central bank hiked rates by 1.25% to 2.75%, amid growing inflationary pressures in the country. The move was bigger than projected by analysts. But the central bank did not provide any concrete signals on whether it intended to keep hiking rates. Still, the move brings lending rates in Chile closer to its emerging market peers, which is likely to benefit the peso. Expectations of tapering in the United States grew after data showed a steep decline in weekly jobless claims, while a separate reading showed producer price inflation on the rise. Tapering of stimulus measures will push up lending rates in the developed world, which in turn tends to make emerging market assets appear less attractive. Mexico"s peso fell 0.4% to the dollar, the most among its regional peers, while Colombia"s peso shed 0.3%. Among Latin American stocks, Brazilian oil and gas firm Petrobras rose 1% as President Jair Bolsonaro said he was inclined to take the firm private, while also outlining possible regulations on local fuel prices. But Brazil"s Bovespa index was weighed down by losses in financial stocks. Key Latin American stock indexes and currencies: Latest Daily % change MSCI Emerging Markets 1267.00 0.54 MSCI LatAm 2249.82 0.96 Brazil Bovespa 113483.34 0.02 Mexico IPC 51985.65 0.33 Chile IPSA 4016.11 0.24 Argentina MerVal - - Colombia COLCAP 1397.63 0.24 Currencies Latest Daily % change Brazil real 5.4951 0.22 Mexico peso 20.6225 -0.36 Chile peso 815.58 -0.09 Colombia peso 3748.03 -0.28 Peru sol 3.97 -0.12 Argentina peso 99.1500 -0.02 (interbank) (Reporting by Ambar Warrick; Editing by Giles Elgood)