* U.S. corn, soy crop ratings improve as harvest gets going

* Dollar rally adds to export worries after storm disruption

* Soybeans climb after reaching three-month low

CHICAGO, Sept 21 (Reuters) - Chicago corn eased for a fourth session on Tuesday as harvest progressed in the United States, pressuring supplies, while a rallying dollar and lingering storm disruption cooled export sentiment.

Wheat tracked corn lower on outside market pressure, while soybeans firmed after a near three-month low on Monday.

The most-active corn contract on the Chicago Board Of Trade (CBOT) ended 4-3/4 cents lower at $5.17 a bushel.

CBOT wheat lost 10-1/2 cents at $6.90-1/4 a bushel.

Soybeans ended down 11-1/2 cents at $12.74 after falling to $12.57-1/2, their lowest since June 18.

The U.S. Department of Agriculture (USDA) said after Monday's market close that the U.S. corn harvest was 10% complete, ahead of the five-year average of 9% for this time of year.

The USDA rated 59% of the U.S. corn crop in good-to-excellent condition, up 1 percentage point from the previous week, while also raising its soybean good-to-excellent score by 1 point to 58%. Analysts on average had expected no change to either rating.

"We’re just getting some harvest pressure in here," said Dan Smith, senior risk manager at Top Third Ag Marketing.

The crop update tempered supply worries that had helped push corn to a two-week high last week.

The dollar index hit a one-month peak on Monday in a rush to safety as investors fretted over the risk of a default by property developer China Evergrande. The U.S. currency edged lower on Tuesday.

A stronger dollar makes U.S. grains less attractive to overseas buyers.

U.S. grain shipments have waned following damage to U.S. Gulf Coast terminals caused by last month's Hurricane Ida.

USDA data on Monday showed corn export inspections were down 48% from the same week a year ago, while soybean inspections were down 80%.

However, in a sign activity was resuming, U.S. corn and soy exports increased from the previous week, the data showed.

Traders are watching to see if a run of U.S. soybean sales to China gathers pace as the U.S. harvest advances.[

"After the rain goes through in the east, it's going to be a wide open stretch of harvest for a week to 10 days across the country," said Chuck Shelby, president of Risk Management Commodities. "Market’s hanging in pretty good at these price levels, considering we’re at harvest." (Reporting by Christopher Walljasper; additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Emelia Sithole-Matarise and Dan Grebler)