Android Spring File Upload OutofMemory

I am trying to use the following code to upload a file to a rest api. This code works fine for files up to around 20MB, but bigger files will give an OutOfMemoryError. I am trying to chunk the request and use a multipart-form request so that I don't have to keep the whole file in memory, but maybe the chunks are too big? Any help is greatly appreciated.

    final File file = new File(filePath);
    HttpHeaders header = new HttpHeaders();
    header.add("x-haiku-auth", HaikuAPI.getAuthHeader());
    header.setContentType(MediaType.MULTIPART_FORM_DATA);
    UriComponentsBuilder builder = UriComponentsBuilder.fromUriString(
            "https://" + HaikuAPI.getDomain() + "/api/assignments")
            .pathSegment(assignmentID + "", "submit");

    URI url = builder.build().toUri();

    MultiValueMap<String, Object> parts = new LinkedMultiValueMap<String, Object>();

    parts.add("message[subject]", "Assignment Completed");
    parts.add("message[body]", message);
    parts.add("message[assignment_id]", assignmentID + "");
    Uri uri = Uri.fromFile(file);
    InputStreamResource res = new InputStreamResource(context.getContentResolver().openInputStream(uri)) {
        @Override
        public String getFilename() throws IllegalStateException {
            return file.getName();
        }

        @Override
        public long contentLength() throws IOException {
            return file.length();
        }
    };
    parts.add("files[][file]", res);
    parts.add("files[][filename]", file.getName());
    SimpleClientHttpRequestFactory factory = new SimpleClientHttpRequestFactory();
    factory.setChunkSize(1024);
    RestTemplate restTemplate = new RestTemplate(factory);
    restTemplate.getMessageConverters().add(new FormHttpMessageConverter());
    HttpEntity<Object> request = new HttpEntity<Object>(parts, header);
    restTemplate.postForLocation(url, request);
    Log.e("f", "finished");
    return null;

Error: dalvikvm-heap: Out of memory on a 67102090-byte allocation.