Put some salt on a flat dish. Moisten the rim of the margarita glass with the lime wedge and dip it in to the salt.
Fill a cocktail shaker with ice. Add the tequila, lime juice, simple syrup and green chile juice to the shaker and shake vigorously for 3 seconds. Pour into the salted glass and garnish with the lime wedge.
To make the simple syrup, heat 1 part water and 1 part granulated sugar in a small saucepan until the sugar dissolves. Cool before using. To prepare the green chile juice, put 1 New Mexico green chile in a blender with 1 ounce of water and blend thoroughly. Strain the puree through a fine mesh strainer and transfer to a squeeze bottle. If New Mexico green chiles are not available, serrano chiles may be substituted.