This claim is false. Grocery prices in the United States have gone up since Trump took office. According to an article titled Fact Check: Grocery prices are up not "way down" as Donald Trump claimed by CNN, "average grocery prices rose 0.3% from August to September... that increase followed a 0.6% jump from July to August, which was the biggest month-to-month jump in three years." It goes on to say that Average grocery prices in September were about 2.7% higher than they were a year prior and about 1.4% higher than they were in January, the month Trump returned to office."
Given this information it is not hard to conclude that the claim is false, however I will attach another article for further proof.
I wanted to include an entirely statistical source, so here is the Consumer Price Index by the U.S. Bureau of Labor Statistics, last updated 09/25. Here is an excerpt I found that sums it up:
"The index for food rose 0.2 percent in September, after rising 0.5 percent in August. The food at home index increased
0.3 percent over the month. Four of the six major grocery store food group indexes increased in September. The index for
other food at home rose 0.5 percent over the month after rising 0.1 percent in August. The cereals and bakery products
index and the nonalcoholic beverages index both increased 0.7 percent in September. The index for meats, poultry, fish,
and eggs rose 0.3 percent over the month following a 1.0-percent increase in August."
Food prices are increasing in the U.S, therefore, this claim is false.