Lightly crush shallots, chilis and lemongrass with a rolling pin or pestle.
Place a wok over medium-high heat. Add shallots, chilis, lemongrass and galangal to wok and dry roast until fragrant, about 1 minute.
Add broth, tamarind paste and lime leaves to wok and bring to a simmer. Add chicken to simmering broth and cook 1 minute. Add coconut milk. Bring soup back to a low simmer and cook until chicken is cooked through.
Add fish sauce, palm sugar and chili paste, stirring to combine. Continue to cook for 2 minutes. Taste and adjust seasoning. Turn off heat and add lime juice. Remove and discard lemongrass stalks and shallots. Serve immediately.