B737 Captain reported conducting a no flap landing after the flaps would not deploy and noted the aircraft was signed off by maintenance for the same issue a day prior to the flight.

Narrative

During arrival phase at ZZZ we went to select flaps 1 and nothing moved. Flap indications were normal (indicator aligned) during preflight; and flaps deployed normally for takeoff. After takeoff the flaps retracted normally; and there was no adverse or abnormal trim required for flight. The indicator showed a slight split that we saw during cruise. In anticipation of a potential problem; the FO (First Officer; Pilot Monitoring) and I reviewed the flap scenarios from the QRH enroute 'just in case' the flaps didn't extend and were somewhat prepared for this. The WX was good; and we had extra ferry fuel to play with. When ATC wanted us to slow during the arrival phase we were unable. We [advised ATC] and asked for a vector while we ran a checklist. They vectored us downwind to an area and gave us box vectors over the lake. We initially went with the Trailing Edge Flap Asymmetry checklist; which took us to the Trailing Edge Flaps Up Landing Checklist due to the Lever being UP to match the closest flaps setting. The leading edge devices deployed correctly using the alternative method IAW the checklist. I briefed the FAs as to the situation and the precautionary landing IAW the non-routine landing considerations and briefed the passengers of the situation and that we would be doing a faster than normal landing and that safety vehicles would be present to inspect the brakes due to the speed. We attempted to contact ZZZ ops to no avail; and I was unsure if crew phone would work at 4K'; so I elected to bypass that part. With checklists complete; and a pause to make sure we were both in the loop and comfortable with the scenario thus far; we advised ATC we were ready for the approach to 28C with flaps up; leading edge devices extended. We had also previously requested response vehicles at the runway out of an abundance of caution and to inspect the brakes due to the speed of the landing. We were below max landing weight. Approach was as normal as you can get for the situation; the landing was smooth; and I applied judicious brakes to go along with the reversers. We taxied clear of the runway with several thousand feet remaining. I reminded the pax to remain seated while we had the brakes inspected; then taxied to the gate normally. After deplaning I held the crew for a quick debrief and to let a couple of them decompress. After landing the flaps indicator aligned back normally; however I made sure the write up indicated the split. Aircraft had previous write up for flaps not deploying; which was signed off by maintenance the day prior. The write up did not indicate an asymmetry; or even if the aircraft had been in flight when it occurred. On another note; the FO (PM) did an outstanding job of pacing; monitoring; and working through the processes. The ZZZ personnel were very supportive and present quickly when we got to the gate. I don't think I could set up a more 'like a simulator' scenario if I tried. We had enough of a break to decompress a bit and were fit to continue the day. Maintenance unable to replicate previous condition as it was written in the logbook. Given that everything worked normally until it didn't; I don't think I have preventive measures for this incident. This is why we get trained and paid.