Many fast microcontrollers can do this or you could 'easily' implement an FPGA solution. Enough such solutions exist that it's just a matter of finding the one that best suits.
I imagine that FPGA vendors offer VGA implementations as library items.
A typical example of a minimalist microcontroller based solution is the "Maximite" which uses a PIC32 processor.
The colour Maximite uses a PIC32 +
Colour Maximite circuit diagram here
The maximum resolution is below what you would desire BUT is essentially a function of available memory and processing resources.
Colour Maximite home page
Building ...
Monochrome VGA - Monochrome Maximite page here
See above page for more details, but they say:
The video is generated by a standard SPI peripheral within the PIC32 chip. This is continuously fed with data by the DMA circuitry which reads a section of memory and feeds the data to the SPI peripheral so that there is a constant stream of ones and zeroes being clocked out on pin 6 of the chip. These bits represent the video signal for a horizontal line with each bit being a pixel. The beauty of this scheme is that it happens independently of the CPU which only needs to write the required pixel data to the allocated section of memory and service an interrupt for the horizontal sync pulse.
The technique is described by Lucio Di Jasio in his book "Programming 32 bit microcontrollers in C” which is well worth reading if you are interested in learning more about programming for the PIC32.
An important part of the circuit is R5 which feeds the horizontal sync pulses back to the SPI peripheral so that the start of the data stream is synchronised to the pulse. This removes any jitter that may be caused if the CPU was used to start the data stream and results in a very steady image on the screen.
Choose a suitable main processor and you have a zero added chip solution.
Undergrad project VGA in FPGA
.png){kind=link}