What is the value of an 1873 US 20 dollar gold piece?

An 1873 double eagle should be examined in person by a knowledgeable dealer or appraiser. There are multiple varieties that can be worth very different amounts, especially in better grades.

For a coin in average condition, you'll need to know the mint mark. Look on the back of the coin to see if there's a small letter below the eagle. It may be blank or there may be an S or a CC.

Numismedia lists the following approximate retail values as of 02/2015:

Philadelphia (no mint mark):

Moderately worn - $1,580

Slightly worn - $1,600

Coins in better condition can range from $2,160 to $1,620,000 (!) depending on the variety

"CC" mint mark (Carson City):

Very worn - $2,250

Moderately worn - $2,530

Slightly worn - $2,940

Almost no wear - $20,438

Uncirculated - $46,150 to $1,282,500

"S" mint mark (San Francisco):

Moderately worn - $1,580

Slightly worn - $1,600

Coins in better condition can range from $1,900 to $30,400 depending on the variety

DISCLAIMER: The retail values quoted are the best available as of the date shown, but may vary significantly due to changes in the precious metals market. Also the wholesale (buying) price of a coin will be less than the selling (retail) price. A reputable coin dealer will be able to give a more accurate valuation based on inspection of the coin.