* CBOT wheat at 3-year low after data show stockpiles above trade estimates

* U.S. soybeans supplies at 2-year low but at high end of forecasts

Sept 29 (Reuters) - Chicago grain and soybean futures fell sharply on Friday, with wheat hitting a three-year low after U.S. government data pegged production above analysts' expectations.

The U.S. Department of Agriculture (USDA) estimated the nation's wheat harvest at 1.812 billion bushels, 78 million bushels bigger than a previous estimate and significantly above the average analyst forecast of 1.729 billion bushels in a Reuters poll.

Chicago Board of Trade wheat futures dropped more than 6% by 12:50 pm CDT (1750 GMT) to $5.42-3/4 a bushel and set the lowest level since Sept. 28, 2020, on a continuous chart.

Futures also hit life-of-contract lows. K.C. hard red winter wheat, which hit two-year lows earlier in the week, continued to fall, trading down 20 cents to $6.65.

"The wheat balance sheets aren't nearly as tight as had been indicated," said Karl Setzer, brokerage research lead for Mid-Co Commodities.

Wheat prices had already been under pressure from ample Russian supplies and signals that Ukraine was managing to find export routes despite Russian attacks on port facilities.

In a separate report, the USDA said U.S. wheat stocks as of Sept. 1 stood at 1.780 billion bushels, up slightly from 1.778 billion bushels reported a year earlier and reflecting poor export demand for U.S. supplies. Analysts had been expecting wheat stocks at a 16-year low of 1.772 billion bushels.

"It is simply another piece of bad news," said Rich Nelson, chief strategist for Allendale.

U.S. soybean stocks fell to their lowest in two years, but were larger than analysts expected. CBOT soybean futures fell nearly 1.5% to $12.80-3/4 a bushel.

"It's still an extremely tight number," said Setzer, "but it gives us much more of a cushion going forward than what we had."

CBOT corn futures followed wheat and soybeans lower, trading down just over 2% at $4.78-1/4 a bushel. (Reporting by Zachary Goelman in New York; Additional reporting by Karl Plume in Chicago, Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Andrea Ricci)