How many grams is a quarter cup of chopped hazelnuts?

A quarter cup of chopped hazelnuts weighs

29g

That's 1oz. In a 250ml metric cup it's 30g.

This uses the US cup, the size American recipes mean. A quarter cup is 59ml by volume.

Other amounts of chopped hazelnuts

1 cup: 115g
Half a cup: 58g
1 tablespoon: 7.2g
Full table for chopped hazelnuts

Where these numbers come from

USDA FoodData Central, SR Legacy, food 12120: “Nuts, hazelnuts or filberts”. USDA lists these household measures for it:

1 cup, chopped = 115g
1 cup, ground = 75g
1 cup, whole = 135g
1 oz (21 whole kernels) = 28.35g
10 nuts = 14g

Fractions of a cup are the cup weight scaled down. The tablespoon figure is the cup weight divided by 16, since USDA doesn't list a tablespoon for this ingredient. The teaspoon is a third of the tablespoon. Metric-cup figures assume a 250ml cup, and Australian tablespoons hold 20ml. Weights under 10g are rounded to 0.1g, everything else to the nearest gram. Full source list.