Delta and Korean Air have code-shared round-trip flights from Dallas (DFW) to Chiang Mai or Singapore (CNX, SIN) for $691-$724 with a connection. Chiang Mai flights February to March. Singapore flights March and April. No weekend departures. 7-day minimum stay required.
Singapore availability is very calendar limited.
Some small OTAs on Skyscanner have this for as low as $691; which is cheaper than the airline.