Combine all ingredients except the oil and chicken in a medium bowl and whisk to combine.
Slowly drizzle the oil into the mixture while whisking continuously until the marinade is emulsified.
Add the chicken to the bowl and toss to coat thoroughly, or transfer the marinade and chicken to a resealable plastic bag and massage to combine.
Refrigerate and marinate the chicken for 2 to 24 hours (up to 48 hours only if necessary); a 30-minute soak will impart some flavor but 12–24 hours is preferred.
Alternative blender method: halve the garlic and shallot amounts, place all ingredients except the chicken in a blender, and blend on high until emulsified. Transfer to a bowl and combine with the chicken as above.
To pan-sear: heat 1–2 tablespoons oil in a non-stick skillet over medium–medium-high heat. Cook the chicken about 6–7 minutes per side, adjusting heat to avoid burning, until internal temperature reaches 165°F for white meat or 175°F for dark meat.
To grill: preheat grill to medium–medium-high (about 325–350°F). Grill chicken 6–7 minutes per side with the lid closed, rotating 90° halfway through the first side for grill marks, until internal temperature reaches 165°F for white meat or 175°F for dark meat.
Remove cooked chicken and let rest for 3–4 minutes before serving.