WordWeb Online

1. Not beset by troubles, disturbance or distress
   "seemed untroubled by doubts of any kind"; "untroubled sleep"; "a kind untroubled face"
    
2. Free from fear or doubt; easy in mind
   - secure, unafraid
    
3. Free from turmoil or worries
   "untroubled times"
    
4. Free from emotional agitation or nervous tension
   "the waiters were untroubled and good natured";
   - unflurried, unflustered, unperturbed, unruffled, unfazed [informal]

See also: carefree, clear, composed, dreamless, quiet, trouble-free, unconcerned, undisturbed, unharassed, unmolested, unworried

Antonym: insecure, troubled