* C$ at C$1.0353 vs US$, or 96.59 U.S. cents * Russia proposes Syria hand over chemical weapons, could avert planned U.S. strike * Chinese retail sales and factory output data positive * Canada housing starts fall more than expected in August * Bond prices fall across curve TORONTO, Sept 10 (Reuters) - The Canadian dollar strengthened to a three-week high versus its U.S. counterpart on Tuesday as tensions eased over a possible U.S. military strike on Syria. U.S. President Barack Obama said on Monday he saw a possible breakthrough in the Syrian crisis after Russia proposed Syria hand over its chemical weapons for destruction, potentially averting planned U.S. military strikes. Still, Obama remained skeptical and is pushing to persuade a divided Congress to back potential action, saying the threat of force was still necessary. "The markets are very risk-positive today," said Adam Cole, global head of FX strategy for RBC Capital Markets in London. "The markets seem to be worrying a lot less about the Middle East, which has generally given asset markets a positive tone that has spilled over into FX." Meanwhile, encouraging Chinese retail sales and factory output data also provided a further boost for more upbeat investor sentiment. The Canadian dollar was trading at C$1.0353 versus the U.S. dollar, or 96.59 U.S. cents at 9:36 a.m. (1336 GMT), stronger than Monday's session close at C$1.0373, or 96.40 U.S. cents. The Canadian dollar touched its strongest level against the Japanese yen since July 27. The currency, which Cole said is expected to trade between C$1.0320 and C$1.0370, eased away from earlier gains to C$1.0331, or 96.80 U.S. cents, its firmest level since August 19. Canadian housing starts fell more than expected in August to hit their lowest since April, hurt primarily by slower condo construction, according to data released on Tuesday that tempered property bubble fears. Prices for Canadian government debt fell across the maturity curve, with the two-year bond slipped 4 Canadian cents to yield 1.309 percent and the benchmark 10-year bond shedding 51 Canadian cents to yield 2.812 percent.