The chip you've linked is capable of analog FM transmission and reception, from 2.5kHz to 80kHz bandwidth. In the frequency range you're looking at it has a frequency resolution of 12.5kHz. It's very low power, with the right antenna it should reach your target LOS. Check out Figure 4.2 in the TH7122 and TH71221 Cookbook for an example showing how to use the chip as an analog FM transmitter, and figure 6.7 for an example of how to use it as an FM receiver. By combining the two circuits with the typical application circuit you can build a single-chip analog FM transceiver.
Note that your requirement, "Single chip that doesn't require extra elements as crystal or filters" is going to be hard to meet with any radio design. There are several inductors and capacitors used as filters outside most "single chip" transceivers. If you want any frequency stability you're going to need a crystal.
The Philips SA58646 is also a good choice, but again you're going to have to deal with a few inductors, capacitors, and a crystal.
Also note that with such low power devices your antennas are going to have to be very, very good, and probably very large. If you don't want to spend a lot of time and effort on antennas, or need small antennas, then you'll have to trade off some additional effort adding an RF amplifier to these devices and consuming more power.
Are you sure you don't simply want an off-the-shelf transceiver? If you're trying to avoid filters and crystals while building your own transceiver, it seems you might need a higher level solution than a DIY circuit. The radio linked is a cheap HT for the UHF band, runs on 3.7V, and has a 3W output. It's under $20, and if you remove the battery, casing, controls, connectors, then the one or two PCBs that are left are very small. It does appear to have a low power TX setting, so you should be able to set it to 1W output rather than the full output power if you have power consumption concerns beyond requiring low voltage. You may even consider modifying the radio to remove the PA and use the very low output prior to the PA, saving significantly more power.